EXHIBIT 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, R. Scott Rowe, President and Chief Executive Officer of Flowserve Corporation (the “Company”), certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

(1) the Annual Report on Form 10-K of the Company for the period ended December 31, 2019, as filed with the Securities and Exchange Commission on the date hereof (the “Annual Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)the information contained in the Annual Report fairly presents, in all material respects, the consolidated financial condition and results of operations of the Company.

/s/  R. Scott Rowe

R. Scott Rowe

President and Chief Executive Officer

(Principal Executive Officer)

Date: February 17, 2020