FORM 4 Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940

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1. Name and Address of Reporting Person * Wilson Kirk   2. Issuer Name and Ticker or Trading Symbol FLOWSERVE CORP [FLS] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director _____ 10% Owner __X__ Officer (give title below) _____ Other (specify below) President, AMSS (Last) (First) (Middle) 5215, NORTH O'CONNOR BLVD #2300 3. Date of Earliest Transaction (Month/Day/Year) 02/27/2019 (Street) IRVING, TX 75039 4. If Amendment, Date Original Filed(Month/Day/Year) 6. Individual or Joint/Group Filing(Check Applicable Line) _X_ Form filed by One Reporting Person ___ Form filed by More than One Reporting Person (City) (State) (Zip) Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned

1.Title of Security (Instr. 3) 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code (Instr. 8) 4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5) 5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4) 6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4) 7. Nature of Indirect Beneficial Ownership (Instr. 4) Code V Amount (A) or (D) Price Common Stock 02/28/2019   M   2,442 (1) A $ 0 34,910 D   Common Stock 02/28/2019   F   595 D $ 44.41 34,315 D

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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)

1. Title of Derivative Security (Instr. 3)

2. Conversion or Exercise Price of Derivative Security

3. Transaction Date (Month/Day/Year)

3A. Deemed Execution Date, if any (Month/Day/Year)

4. Transaction Code (Instr. 8)

5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4, and 5)

6. Date Exercisable and Expiration Date (Month/Day/Year)

7. Title and Amount of Underlying Securities (Instr. 3 and 4)

8. Price of Derivative Security (Instr. 5)

9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)

10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)

11. Nature of Indirect Beneficial Ownership (Instr. 4)

Code

V

(A)

(D)

Date Exercisable

Expiration Date

Title

Amount or Number of Shares

Restricted Stock Units

(1)

02/27/2019

A

7,760

(1)

(1)

Common Stock

7,760

$ 0

16,985

D

Restricted Stock Units

(1)

02/28/2019

M

2,400

(1)

(1)

Common Stock

2,400

$ 0

14,585

D

Performance Rights

(2)

02/27/2019

A

7,760

(2)

(2)

Common Stock

7,760

$ 0

30,290

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
Wilson Kirk 5215 NORTH O'CONNOR BLVD #2300 IRVING, TX 75039			President, AMSS

Signatures

/s/ Akshar C. Patel, attorney-in-fact		03/01/2019
**Signature of Reporting Person		Date

Explanation of Responses:

*	If the form is filed by more than one reporting person, see Instruction 4(b)(v).
**	Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1)	Each restricted stock unit represents the right to receive, at settlement, one share of common stock (plus dividends accrued on the underlying shares) and are granted to the reporting person pursuant to the issuer's long-term incentive compensation plan for employees. The shares vest ratably over a three-year period on each annual anniversary of the grant.
(2)	Each performance right represents a contingent right to receive one share of the issuer's common stock at vesting. The performance rights vest at a rate between 0% and 200% and are based on two factors during a three-year performance cycle beginning on January 1, 2019 and ending on December 31, 2021 which are: 1) the issuer's relative total shareholder return ("TSR") in comparison to the TSR averages of a predetermined compensation peer group over the performance cycle; and 2) the issuer's return on invested capital ("ROIC") measured against the issuer's ROIC improvement goals under its operating plan. The performance rights may be settled, at the issuer's discretion, in cash or shares of common stock.

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