FORM 6-K

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D. C. 20549

                        Report of Foreign Private Issuer
                      Pursuant to Rule 13a-16 or 15d-16 of
                       the Securities Exchange Act of 1934

                           For the month of May, 2004

                           A/S STEAMSHIP COMPANY TORM
                 (Translation of registrant's name into English)

                                   Marina Park
                                Sundkrogsgade 10
                              DK-2100 Copenhagen 0
                                     Denmark
                    (Address of principal executive offices)

     Indicate by check mark whether the registrant files or will file annual
reports under cover Form 20-F or Form 40-F.

                           Form 20-F |X| Form 40-F |_|

         Indicate by check mark whether the registrant by furnishing the
information contained in this Form is also thereby furnishing the information to
the commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of
1934.

                                 Yes |_| No |X|


INFORMATION CONTAINED IN THIS FORM 6-K REPORT

          Set forth herein 1) as Exhibit 1 is a copy of a Announcement No. 9 -
2004 TORM - Results for first quarter 2004 issued by A/S STEAMSHIP COMPANY TORM
(the "Company") to The Copenhagen Stock Exchange (the "Exchange") on May 19,
2004, 2) as Exhibit 2 is a copy of a Share Statement No. 9 - 2004 issued by the
Company to the Exchange on May 24, 2004 and 3) as Exhibit 3 is a copy of a Share
Statement No. 10 - 2004 issued by the Company to the Exchange on May 25, 2004.


Exhibit 1
---------

ANNOUNCEMENT NO. 9- 2004

19 May 2004

TORM - results for first quarter 2004 - Expectations for 2004 of profit before
tax on own activities of minimum DKK 750-800 mill.

o    Profit from own activities was DKK 249 mill., which was better than
     expected and is considered highly satisfactory.

o    Profit after tax for the first quarter of 2004 was DKK 1.096 mill.,
     including value adjustment on the NORDEN shares of DKK 847 mill. The value
     adjustment on the NORDEN shares has from the end of first quarter 2004 to
     18 May 2004 decreased to DKK 506 mill.

o    Profit before depreciation was DKK 317 mill. for the first quarter 2004
     (DKK 139 mill. for the first quarter of 2003).

o    Profit before financial items was DKK 267 mill. for the quarter (DKK 87
     mill.).

o    Cash flow from operating activities was DKK 308 mill. (DKK 95 mill.).

o    Return on invested capital was 31.9% p.a. and return on equity was 145.6%
     p.a. for the quarter. Shareholders' equity totalled DKK 3,559 mill. as at
     31 March 2004.

o    Freight rates in the Tanker division have for the first quarter and into
     the second quarter 2004 been above the expectations in the Annual Report
     2003. In the Bulk Division, freight rates have been in line with the
     expectations in the first quarter 2004 but below expectations in the
     beginning of the second quarter.

o    Pre tax profit expectations for 2004 are minimum DKK 750-800 mill. before
     any value adjustments related to the shares in Dampskibsselskabet `NORDEN'
     A/S.

A telephone conference reviewing the results will take place on Monday 24 May
2004 at 17.00 hours Danish time to review the results. The telephone conference
will also be accessible via the Internet (www.torm.com). In order to participate
please call 10 minutes prior to the start of the telephone conference on +45 32
71 46 11 (from Europe) or +1 334 420 4950 from the U.S.

A/S Dampskibsselskabet TORM

Contact persons:    Klaus Kjaerulff, CEO (tel.: +45 39 17 92 00)
                    Klaus Nyborg, CFO (tel.: +45 39 17 92 00)



KEY FIGURES FOR THE GROUP

---------------------------------------------------------------------------------------
DKK mill.
                                                     q1      q1   Change q1   Full year
                                                   2004    2003     2003-04        2003
---------------------------------------------------------------------------------------
                                                                     
INCOME STATEMENT
Net revenue                                         610     502         22%       1,928
Time Charter equivalent earnings                    487     317         54%       1,307
Gross profit                                        333     153        118%         647
Profit before depreciation                          317     139        128%         572
Profit before financial items                       267      95        181%         395
Net gain/(loss) from other investments and
   securities                                       851      10       8725%         682
Other financial items                               -22      -4        548%         -25
Profit/(loss) before tax                          1,096     101        985%       1,052
Net profit after tax for the period               1,096     101        985%       1,051
---------------------------------------------------------------------------------------
BALANCE SHEET
Total assets                                      6,228   4,159         50%       4,894
Shareholders' equity                              3,559   1,674        113%       2,464
Liabilities                                       2,669   2,485          7%       2,430

Invested capital                                  3,509   2,932         20%       3,186
Net interest bearing debt                         1,774   1,562         14%       1,698
---------------------------------------------------------------------------------------
CASH FLOW
From operating activities                           308      87        254%         494
From investing activities                          -311    -217         43%      -1,008
   thereof investment in tangible fixed assets     -311    -328         -5%      -1,122
From financing activities                           154     182        -15%         471
                                                    ---     ---                     ---
Net cash flow                                       151      52        190%         -43
---------------------------------------------------------------------------------------
KEY FIGURES
Gross margin                                      54.6%   30.5%                   33.6%
Profit before depreciation/Net revenue            52.0%   27.7%                   29.7%
Profit before financial items/Net revenue         43.8%   18.9%                   20.5%
RoE (p.a.)                                       145.6%   24.5%                   51.4%
RoIC (p.a.)                                       31.9%   13.2%                   13.1%
Equity ratio                                      57.1%   40.3%                   50.3%

Share price, end of period (DKK)                  356.4    65.8        442%       180.5
Millions of shares, end of period                  18.2    18.2          0%        18.2
Earnings per share (DKK)                           63.2     5.8        984%        60.7
Exchange rate USD/DKK, end of period               6.09    6.82        -11%        5.96
Exchange rate USD/DKK, average                     5.96    6.92        -14%        6.59

---------------------------------------------------------------------------------------



FIRST QUARTER 2004 RESULTS

Profit from own activities was DKK 249 mill.  Profit after tax for first quarter
2004 was DKK 1,096 mill., including value adjustment on the NORDEN investment of
DKK 847 mill.

Gross profit for the first quarter of 2004 was DKK 333 mill. (as against DKK 153
mill. for the first quarter 2003).  The increase was primarily the result of the
net effect of higher  freight rates  achieved by the Tanker  Division,  a strong
increase in freight rates in the Bulk Division, an increased number of available
operating  days for both the Tanker and Bulk  divisions  due to the  delivery of
vessels, countered by a 14% reduction in the USD/DKK exchange rate in comparison
with first quarter 2003.

Profit before depreciation was DKK 317 mill. (DKK 139 mill.).

Depreciation  was DKK 50 mill.  (DKK 44 mill.).  The increased  depreciation  is
brought  about by an increase in the  Company's  fleet  through the  delivery of
three  product  tanker  newbuildings  and two second  hand bulk  carriers in the
period April 2003 to March 2004, offset by the lower USD/DKK exchange rate.

Net financial items were positive by DKK 829 mill. (DKK 6 mill.). These included
net gains on securities - primarily  the NORDEN  shares - of DKK 851 mill.,  net
interest expense of DKK 16 mill. less other financial items of minus DKK 6 mill.

Profit before tax was DKK 1,096 mill. (DKK 101 mill.).

Profit after tax was DKK 1,096 mill. (DKK 101 mill.)

The Tanker  Division's  net profit  was DKK 125 mill.  whilst the Bulk  division
showed a net profit of DKK 121 mill.  Other  activities - primarily  unallocated
financial items - generated after tax profits of DKK 850 mill.

Cash flow from  operating  activities  was positive by DKK 308 mill.  during the
first quarter of 2004 and consisted primarily of cash operating earnings.

Cash flow from investments was negative by DKK 311 mill.,  mainly  consisting of
investments in fixed assets, primarily vessels.

Cash flow from  financing  activities was DKK 154 mill. for the first quarter of
2004. This amount  consists  primarily of loan draw-downs in connection with the
delivery of newbuildings and second hand vessels  totalling DKK 425 mill.,  less
repayments of mortgage and leasing debt of DKK 250 mill.

Net cash flow for the first quarter of 2004 was DKK 151 mill. The Company's cash
and bond  holdings  totalled DKK 630 mill.  against DKK 479 mill.  at the end of
2003.

Total  assets rose during the  quarter  from DKK 4,894 mill.  to DKK 6,228 mill.
primarily  due to an increase in fixed  assets  during the period from DKK 4,169
mill. to DKK 5,354 mill.  This positive effect was principally the result of the
delivery in January 2004 of TORM Estrid, the increase in the value of the NORDEN
investment  and the  increase in the USD/DKK  exchange,  offset by  depreciation
during the period.  The  investment  in NORDEN is valued at a price of DKK 2,469
per share, which was the closing price on the Copenhagen Stock Exchange as at 31
March 2004.

The Company's net interest  bearing debt  increased  during the first quarter of
2004 from DKK 1,698 mill.  to DKK 1,774 mill.  The  increase  is  primarily  the
result of net loan draw-downs in connection  with the delivery of  newbuildings,
countered by the positive cash flow for the period.

During the first quarter of 2004,  equity rose from DKK 2,464 mill. to DKK 3,559
mill.  mainly  brought about by earnings  during the period.  The  percentage of
equity to total assets rose from 50.3% as at 31 December  2003 to 57.1% as at 31
March 2004.

As at 31 March 2004, TORM owned 787,376 own shares,  which is equivalent to 4.3%
of the  Company's  share  capital.  The number of owned  shares  decreased  from
881,368  shares as at 31 December  2003 as a result of exercise of options under
the Company's share incentive programme.


--------------------------------------------------------------------------------------------------
Q1 2004 - segment information (DKK mill.)

                                                          Tanker        Bulk
                                                        division    division   Unallocated   Total
--------------------------------------------------------------------------------------------------
                                                                                 
Net revenue                                                  354         256             0     610
Port expenses and bunker                                     -85         -38             0    -123
                                                             ---         ---             -    ----
Time charter equivalent earnings                             269         218             0     487
Charter hire                                                 -19         -65             0     -84
Operating expenses                                           -55         -15             0     -70
                                                             ---         ---             -     ---
Gross Profit                                                 195         138             0     333
Profit on sale of vessels and interest                         0           0             0       0
Administrative expenses                                      -24          -8            -1     -33
Other Operating income                                        17           0             0      17
                                                              --           -             -      --
Profit before depreciation                                   188         130           - 1     317
Depreciation                                                 -42          -8             0     -50
                                                             ---          --             -     ---
Profit before financial items                                146         122            -1     267
Net gain/(loss) from other investments and securities          0           0           851     851
Other financial items                                        -21          -1             0     -22
                                                             ---          --             -     ---
Profit/(Loss) before tax                                     125         121           850   1,096
Tax                                                            0           0             0       0
                                                               -           -             -       -
Net profit for the period                                    125         121           850   1,096

--------------------------------------------------------------------------------------------------


TANKER DIVISION

Profit after tax in the Tanker Division was DKK 125 mill. for the first quarter.

Freight  rates were at a high  level  during  the first  quarter of 2004,  which
usually is the case  during the winter  season.  Economic  growth and a high oil
price contributed to keeping  continually low stocks of refined products,  which
combined with a relatively cold winter in parts of North America all contributed
to healthy freight rate levels for the Tanker Division.

Compared with the first quarter of 2003,  rates were  respectively  2% lower and
20% and 17% higher for the LR2,  the LR1 and the MR  segments.  The first  three
months of 2004  compared  with the same period in 2003 were not  affected to the
same degree by individual factors but still resulted in very firm rates.

The  combined  activity  level for the  Tanker  Division  expressed  in terms of
available  earning days rose by 21% during the first  quarter of 2004 as against
the same period last year. In the LR2 segment,  the number of available  earning
days rose by 69% from first  quarter  2003 to first  quarter 2004 as a result of
the delivery of two  newbuildings  towards the end of 2003.  In the LR1 segment,
the  increase  was 37%,  reflecting  the  delivery of the TORM Estrid in January
2004, whilst a marginal increase in the number of earning days in the MR segment
was brought about by the delivery of two  newbuildings  during the first quarter
of 2003, and the delivery of TORM Alice in February 2004.

Earnings data for the Tanker division



                                                      2003
                                               ------------------     2004   Change
                                               Full year       q1       q1    q1-q1
LR2/Aframax vessels
-----------------------------------------------------------------------------------
                                                                   
Available earning days                             1,231      270      455      69%
TCE per earning days (USD/Day)*)                  27,185   31,237   32,012       2%
OPEX per earning days (USD/Day)**)                -5,799   -5,651   -4,453      21%
Operating C/F per earning days (USD/Day)***)      13,911   16,931   21,697      28%
-----------------------------------------------------------------------------------

LR1/Panamax vessels
-----------------------------------------------------------------------------------
Available earning days                               847      210      288      37%
TCE per earning days (USD/Day)*)                  22,429   23,630   28,270      20%
OPEX per earning days (USD/Day)**)                -6,458   -5,691   -6,141      -8%
Operating C/F per earning days (USD/Day)***)      15,883   17,939   22,130     -23%
-----------------------------------------------------------------------------------

MR vessels
-----------------------------------------------------------------------------------
Available earning days                             4,015    1,004    1,047       4%
TCE per earning days (USD/Day)*)                  17,307   18,355   21,491      17%
OPEX per earning days (USD/Day)**)                -5,257   -5,701   -5,927      -4%
Operating C/F per earning days (USD/Day)***)      12,051   12,653   15,565      23%
-----------------------------------------------------------------------------------


*)   TCE = Time Charter Equivalent  Earnings = Gross freight income less bunker,
     commissions and port expenses.

**)  Operating expenses for own vessels.

***) TCE earnings less operating expenses and charter hire.


THE BULK DIVISION

The Bulk  Division  achieved  profits  after tax of DKK 121 mill.  for the first
quarter of 2004.  Freight rates in the dry bulk market were at an  exceptionally
high level during the first quarter of 2004 albeit there was a decreasing  trend
towards the end of the quarter and into the second  quarter.  The high rates for
the period were  primarily  the result of very strong  demand from China coupled
with a significant increase in waiting time in many ports.

Freight rates for the first quarter were 153% and 112%  respectively  higher for
TORM's Panamax and Handysize vessels compared to first quarter 2003.

When  freight  rates began to rise  significantly  towards the end of  September
2003, TORM began to cover available  earning days for 2004. This has contributed
to ensuring less volatile earnings for the current year.

The number of available  earning days during first quarter 2004 as compared with
first quarter of 2003  increased by 19% for TORM's  Panamax fleet as a result of
the chartering-in of additional  tonnage,  whilst in the Handysize segment,  one
vessel was  redelivered  during 2003,  which accounts for the decrease of 15% in
the number of available earning days in this segment.

Earnings data for the Bulk Division



                                                     2003            2004   Change
                                              ---------------------------
                                              Full year       q1       q1    q1-q1
Panamax vessels
----------------------------------------------------------------------------------
                                                                 
Available earning days                            5,147    1,161    1,383      19%
TCE per earning day (USD/day)*)                  11,695    9,166   23,219     153%
OPEX per earning day (USD/day)**)                -5,109   -5,208   -5,501       6%
Operating C/F per earning day (USD/day)***)       2,929      606   14,327    2264%
----------------------------------------------------------------------------------

Handysize vessels
----------------------------------------------------------------------------------
Available earning days                            1,258      356      303     -15%
TCE per earning day (USD/day)*)                   8,706    7,526   15,963     112%
OPEX per earning day (USD/day) **)               -3,058   -3,442   -3,112     -10%
Operating C/F per earning day (USD/day)***)       4,135    2,664   11,187     320%
----------------------------------------------------------------------------------


*)   TCE = Time Charter Equivalent  Earnings = Gross freight income less bunker,
     commissions and port expenses

**)  Operating expenses for own vessels.

***) TCE earnings less operating expenses and charter hire.

UNALLOCATED

Unallocated  items  consist  of an amount  of DKK 850 mill.  which is made up of
unallocated  financial items including the unrealised gain on the NORDEN holding
of DKK 847 mill.  Unallocated items furthermore consist of minor items connected
with adjustments related to the Liner activity, which was sold in 2002.

FLEET DEVELOPMENT

During the first quarter of 2004,  TORM took delivery of the LR1 product  tanker
TORM  Estrid,  and  during the same  period  exercised  purchase  options on two
time-chartered vessels, TORM Baltic and TORM Marlene at favourable prices. These
two vessels  will be delivered in the second  quarter  2004.  During the period,
TORM also  purchased the MR product  tanker TORM Alice from the  Company's  pool
partner Rederi AB Gotland.

TORM's order book currently consists of six newbuildings (one LR1 product tanker
due for delivery in the summer of 2004 and five LR2 product tankers for delivery
during 2006-2008) with a total value of more than USD 200 mill.

Since the end of 2003, vessel values have generally increased substantially both
for tankers and bulk carriers.

The  certification of the Company's ships to conform to the so-called ISPS code,
which  consists  of a  number  of  security  requirements  aimed  at the risk of
terrorism described in the Annual Report 2003, is proceeding  according to plan.
As such, more than two thirds of vessels under TORM's  technical  management are
already  certified,  with the remainder  expected to have certification in place
well ahead of the 1 July 2004 deadline.

CHINA

In recent years,  ship owners have placed great emphasis on the Chinese  market.
Within the dry bulk segment, the primary reason for the significant increases in
freight  rates have to a very large degree been the result of a vast increase in
the import to China of raw materials, especially iron ore. China is now also the
world's  second  largest  consumer  of oil and a gradual  liberalisation  in the
import of clean  petroleum  products  is  expected to lead to an increase in the
import of refined  products to the country.  In 2003 alone,  the import of clean
petroleum products to China increased by 50%. China's demand is, however, not as
crucial in the  product  tanker  market,  as the import of refined  products  is
limited, though rapidly increasing.

After the end of the first quarter of 2004,  the Chinese  authorities  adopted a
number of measures  aimed at  avoiding  the risk of  overheating  in the Chinese
economy.  These  measures are expected to result in a more modest Chinese growth
for the remainder of 2004,  but in the medium to long term, the outlook for both
the Chinese and far eastern  markets  generally  continue to look  promising for
shipping.

TORM has during the first quarter of 2004  strengthened  the Company's  existing
organisation in Singapore.  The majority of the Company's activities today is in
the Far East and Middle East and as such,  an  increased  presence  will support
continued growth in this market.

CREWING

In order to achieve greater control over key elements of ship  operations,  TORM
has decided to open its own office in the  Philippines  and thereby  even better
than previously  control the  recruitment and training of Filipino  officers and
seamen. To date, this has been handled by a local crewing agency.

PRODUCT TANKER POOLS

The three product tanker pools  consisted of a total of 63 ships as per 31 March
2004. During the first quarter 2004, the net increase in the three pools was two
vessels. Based on the delivery of vessels already on order, the three pools will
consist of 76 vessels by the end of 2004.

There are on-going  discussions  with a number of potential  partners  about the
possibility of participating in the three pools.

EXPECTATIONS FOR 2004

Freight  rates for the first  quarter  of 2004 and the  beginning  of the second
quarter of 2004 for the Tanker  Division  has been higher  than  expected in the
2003 Annual Report.  The improved freight rate picture is due to the combination
of satisfactory  economic  growth,  historically low inventories for refined oil
products,  together with the removal from the market of a significant  number of
older,  single hulled tankers due for demolition.  The increase in demolition is
due not only to the less favourable  trading conditions for this type of vessel,
but also to the very high scrap prices - reflecting the strong demand for steel.

In the Bulk Division,  freight rates for the first quarter 2004 was in line with
the  expectations   expressed  in  the  2003  Annual  Report,   but  were  below
expectations in the beginning of the second quarter 2004. Due to a slow start to
the grain export from South America  combined with Chinese  action to dampen the
rapid growth in the economy  freight rates were falling towards the end of first
quarter and into second  quarter  2004.  However,  freight rates are still at an
attractive level.

76% of the available  earning days of the Company's Panamax bulk vessels in 2004
were covered at an average rate of USD 24,750 per day, as at 30 April 2004.  The
measures taken in China lead to  expectations  of a continued  strong demand and
thereby  attractive  freight rate levels, as the addition of newbuildings to the
world fleet in the period 2004-06 in both Panamax and Handysize is limited.

Expectations  for  TORM's  profit  before  tax is  minimum  DKK  750-800  mill.,
excluding value adjustments to the NORDEN  shareholding.  The unrealised gain on
the  NORDEN  holding  in 2004 was as at 18 May 2004  DKK 506  mill.,  based on a
NORDEN shares price of DKK 2,000/share.

The forecast is based on a USD/DKK exchange rate of 6.00.


--------------------------------------------------------------------------------
SAFE HARBOUR STATEMENT - FORWARD LOOKING STATEMENTS

Matters  discussed in this release may  constitute  forward-looking  statements.
Forward-looking  statements  reflect  our current  views with  respect to future
events and financial  performance and may include  statements  concerning plans,
objectives,  goals,  strategies,  future events or  performance,  and underlying
assumptions and other statements,  which are other than statements of historical
facts.

The   forward-looking   statements  in  this  release  are  based  upon  various
assumptions,  many of which  are  based,  in  turn,  upon  further  assumptions,
including without limitation,  management's  examination of historical operating
trends,  data  contained  in our  records  and other data  available  from third
parties.  Although TORM believes that these  assumptions  were  reasonable  when
made,   because  these   assumptions  are  inherently   subject  to  significant
uncertainties and contingencies which are difficult or impossible to predict and
are  beyond  our  control,  TORM  cannot  assure  you  that it will  achieve  or
accomplish these expectations, beliefs or projections.

Important  factors  that,  in our view,  could  cause  actual  results to differ
materially from those discussed in the  forward-looking  statements  include the
strength of world  economies and  currencies,  changes in charter hire rates and
vessel  values,  changes in demand for "tonne miles" of crude oil carried by oil
tankers,  the  effect of  changes  in OPEC's  petroleum  production  levels  and
worldwide  oil  consumption  and  storage,  changes  in demand  that may  affect
attitudes of time charterers to scheduled and unscheduled  dry-docking,  changes
in TORM's operating expenses, including bunker prices, dry-docking and insurance
costs, changes in governmental rules and regulations including  requirements for
double  hull  tankers  or actions  taken by  regulatory  authorities,  potential
liability  from  pending  or  future  litigation,   domestic  and  international
political  conditions,  potential disruption of shipping routes due to accidents
and political events or acts by terrorists.

Risks and  uncertainties are further described in reports filed by TORM with the
US Securities and Exchange Commission,  including the TORM Annual Report on Form
20-F and its reports on Form 6-K.
--------------------------------------------------------------------------------


ACCOUNTING POLICIES

The  accounts  for the first  quarter  2004 have  been  prepared  using the same
accounting policies as for the 2003 Annual Report.

The accounting policies are described in more detail in the 2003 annual report.

The quarterly  report for the first  quarter of 2004 is unaudited,  in line with
normal practice.

TELEPHONE CONFERENCE AND WEBCAST

TORM invites financial analysts and investors to a telephone  conference,  where
the quarterly report for first quarter 2004 will be discussed,  on Monday 24 May
2004 at 17.00 hours Danish time. The telephone  conference  will be conducted in
English and will be hosted by Klaus  Kjaerulff,  CEO and Klaus  Nyborg,  CFO. To
participate  please  call  10  minutes  prior  to the  start  of  the  telephone
conference on +45 32 71 46 11 (from Europe) or +1 334 420 4950 from the U.S. The
telephone  conference  will also be accessible via the Internet  (www.torm.com),
from  where  the  presentation  used in the  telephone  conference  can  also be
downloaded.


Income statement

--------------------------------------------------------------------------------
                                                                GROUP
                                                       -------------------------
                                                         First    First
                                                       quarter   quarter    2003
                                                          2004      2003
DKK mill.
--------------------------------------------------------------------------------

Net revenue                                                610       502   1,928
Port expenses and bunkers                                 -123      -185    -621
                                                       -------------------------

Time Charter Equivalent Earnings                           487       317   1,307

Charter hire                                               -84       -95    -405
Technical running costs                                    -70       -69    -255
                                                       -------------------------

Gross profit                                               333       153     647

Profit on sale of vessels and interests                      0         0       0
Administrative expenses                                    -33       -27    -126
Other operating income                                      17        13      51

                                                       -------------------------

Profit before depreciation                                 317       139     572

Depreciation                                               -50       -44    -177
                                                       -------------------------

Profit before financial items                              267        95     395

Net gain/(loss) from other investments
  and securities                                           851        10     682
Other financial items                                      -22        -4     -25
                                                       -------------------------

Profit before tax                                        1,096       101   1,052

Tax                                                          0         0      -1
                                                       -------------------------

Net profit                                               1,096       101   1,051
                                                       =========================

--------------------------------------------------------------------------------


Balance sheet

--------------------------------------------------------------------------------
                                                           GROUP
                                           -------------------------------------
                                           31 March 2004        31 December 2003
DKK mill.
--------------------------------------------------------------------------------

ASSETS
FIXED ASSETS
Tangible fixed assets
Leasehold improvements                                 1                       2
Land and buildings                                     2                       3
Vessels and capitalized dry-docking                3,314                   2,944
Prepayment on vessels under construction             199                     229
Other plant and operating equipment                   14                      15
                                           -------------------------------------
                                                   3,530                   3,193
                                           -------------------------------------

Financial fixed assets
Other investments                                  1,824                     976
                                           -------------------------------------
                                                   1,824                     976
                                           -------------------------------------

TOTAL FIXED ASSETS                                 5,354                   4,169
                                           -------------------------------------

CURRENT ASSETS
Inventories
Inventories of bunkers                                29                      26
                                           -------------------------------------

Accounts receivables
Freight receivables, etc.                            142                     147
Other receivables                                     62                      51
Prepayments                                           11                      22
                                           -------------------------------------
                                                     215                     220
                                           -------------------------------------
Securities
Bonds                                                338                     316
                                           -------------------------------------

Cash at bank and in hand                             292                     163
                                           -------------------------------------

TOTAL CURRENT ASSETS                                 874                     725
                                           -------------------------------------

TOTAL ASSETS                                       6,228                   4,894
                                           =====================================

--------------------------------------------------------------------------------


Balance sheet

--------------------------------------------------------------------------------
                                                                    GROUP
                                                         -----------------------
                                                         31 March   31 December
                                                             2004          2003
DKK mill.
--------------------------------------------------------------------------------


SHAREHOLDERS' EQUITY
Common shares                                                 182           182
Own shares                                                    -46           -52
Retained profit                                             3,205         2,116
Proposed dividend                                             218           218
                                                         -----------------------

TOTAL SHAREHOLDERS' EQUITY                                  3,559         2,464
                                                         -----------------------

LIABILITIES
Long-term liabilities
Mortgage debt and bank loans                                2,096         1,701
Capitalized lease obligations                                   0             0
                                                         -----------------------
                                                            2,096         1,701
                                                         -----------------------

Current liabilities
Next year's repayments on mortgage debt and bank loans        308           295
Capitalized lease obligations                                   0           181
Trade accounts payable                                         78            96
Other liabilities                                             135           102
Accruals                                                       52            55
                                                         -----------------------
                                                              573           729
                                                         -----------------------

TOTAL LIABILITIES                                           2,669         2,430
                                                         -----------------------

TOTAL LIABILITIES AND SHAREHOLDERS' EQUITY                  6,228         4,894
                                                         =======================

--------------------------------------------------------------------------------


Cash flow statement

---------------------------------------------------------------------------

                                                              -------------
                                                              First quarter
                                                                       2004
DKK mill.
---------------------------------------------------------------------------

CASH FLOW FROM OPERATING ACTIVITIES
Profit before financial items                                           267
Interest income, exchange rate gains and dividends received               6
Interest expenses                                                       -22
                                                              -------------
                                                                        251
Adjustments:
Reversal of depreciation and impairment loss                             50
Reversal of other non-cash movements                                     -6
Change in inventories, accounts receivables and payables                 13
                                                              -------------

Net cash inflow from operating activities                               308
                                                              -------------

CASH FLOW FROM INVESTING ACTIVITIES
Investment in tangible fixed assets                                    -311
Investment in equity interests and securities                             0
Sale of fixed assets                                                      0
     including profit on sale of vessels                                  0
     (included in operating activities)
                                                              -------------

Net cash inflow/(outflow) from investing activities                    -311
                                                              -------------

CASH FLOW FROM FINANCING ACTIVITIES
Borrowing, mortgage debt                                                425
Repayment/redemption, mortgage debt                                    -181
Repayment/redemption, lease liabilities                                 -69
Dividends paid                                                            0
Purchase/disposals of own shares                                          6
Settlement share options                                                -27
                                                              -------------

Cash inflow/(outflow) from financing activities                         154
                                                              -------------

Increase/(decrease) in cash and cash equivalents                        151

Cash and cash equivalents,
   including bonds, at 1 January                                        479
                                                              -------------

Cash and cash equivalents,
   including bonds, at 31 March                                         630

---------------------------------------------------------------------------

Shareholders' equity

--------------------------------------------------------------------------------
                                                                       GROUP
                                                                   -------------
                                                                   First quarter
DKK mill.                                                                   2004
--------------------------------------------------------------------------------

Balance at 1 January 2004                                                  2,464
Exchange rate adjustment arose upon translation from
   measurement currency to presentation currency                              31
Fair value adjustment of derivative financial instruments                    -11
Exercise share options                                                       -27
Disposal of own shares at cost                                                 6
Net profit for the period                                                  1,096
                                                                   -------------

Balance at 31 March 2004                                                   3,559

--------------------------------------------------------------------------------


Reconciliation to United States Generally Accepted Accounting Policies (US
GAAP), as of 31 March 2004:

--------------------------------------------------------------------------------
                                                      Net Income   Shareholders'
                                                                       Equity
                                                      --------------------------
DKK mill.

Income/Shareholders' equity as reported under
Danish GAAP                                                1,096           3,559

Dry-docking costs                                              0             -42
Write-down on vessels                                          0             -11
Unrealized gain on marketable securities                    -850               0
Derivative financial instruments                             -12               0
Share options                                                -64             -41
Deferred tax                                                  -1            -356

                                                      --------------------------
Income/Shareholders' equity in accordance with
US GAAP                                                      169           3,109
--------------------------------------------------------------------------------


Exhibit 2
---------

SHARE STATEMENT No. 9 - 2004

24 May 2004

This is to notify you of changes in the shareholdings of the company's  insiders
pursuant according to the Danish Securities Trading Act.

--------------------------------------------------------------------------------
Securities     Trade date   Holding     Market     Total Holding    Total market
  code                      number      value          number           value
--------------------------------------------------------------------------------
DK0010281468   21.05.2004   -12,170  1,992,925.12    1,182,022    193,768,864.00
--------------------------------------------------------------------------------

A/S Dampskibsselskabet TORM
Contact person: Klaus Nyborg, CFO (tel.: +45 39 17 92 00)


Exhibit 3
---------

SHARE STATEMENT No. 10 -2004

25 May 2004

This is to notify you of changes in the shareholdings of the company's  insiders
pursuant according to the Danish Securities Trading Act.

--------------------------------------------------------------------------------
Securities     Trade date   Holding     Market     Total Holding    Total market
  code                      number      value          number           value
--------------------------------------------------------------------------------
DK0010281468   19.05.2004   -1,900   304,950.00      2,370,126    358,315,520.00
--------------------------------------------------------------------------------
DK0010281468   24.05.2004   -6,000   912,000.00      2,370,126    358,315,520.00
--------------------------------------------------------------------------------

A/S Dampskibsselskabet TORM
Contact person: Klaus Nyborg, CFO (tel.: +45 39 17 92 00)


                                   SIGNATURES

          Pursuant to the  requirements of the Securities  Exchange Act of 1934,
the  registrant  has duly  caused  this report to be signed on its behalf by the
undersigned, thereunto duly authorized.

                           A/S STEAMSHIP COMPANY TORM
                                  (registrant)


Dated: May 27, 2004                                 By: /s/ Klaus Nyborg
                                                        -----------------------
                                                        Klaus Nyborg
                                                        Chief Financial Officer

03810.0001 #489519