Exhibit 5.1

Gibson, Dunn & Crutcher LLP   2001 Ross Avenue Dallas, TX 75201-2911 Tel 214.698.3100 www.gibsondunn .com

July 30, 2024

Flowserve Corporation

5215 N. O’Connor Boulevard, Suite 700

Irving, TX 75039

Re: Flowserve Corporation Registration Statement on Form S-8

Ladies and Gentlemen:

We have examined the Registration Statement on Form S-8 (the “Registration Statement”) of Flowserve Corporation, a New York corporation (the “Company”), to be filed with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), in connection with the offering by the Company of up to 4,000,000 shares of the Company’s common stock, par value $1.25 per share (the “Shares”), under the Flowserve Corporation 2024 Employee Stock Purchase Plan (the “Plan”).

We have examined the originals, or photostatic or certified copies, of such records of the Company and certificates of officers of the Company and of public officials and such other documents as we have deemed relevant and necessary as the basis for the opinions set forth below. In our examination, we have assumed the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to original documents of all documents submitted to us as copies. We have also assumed that there are no agreements or understandings between or among the Company and any participants in the Plan that would expand, modify or otherwise affect the terms of the Plan or the respective rights or obligations of the participants thereunder. Finally, we have assumed the accuracy of all other information provided to us by the Company during the course of our investigations, on which we have relied in issuing the opinion expressed below.

Based upon the foregoing examination and in reliance thereon, and subject to the qualifications, assumptions and limitations stated herein and in reliance on the statements of fact contained in the documents that we have examined, we are of the opinion that the Shares, when issued and sold in accordance with the terms set forth in the Plan, as applicable, and against payment therefor in accordance with the terms of the Plan, and when the Registration Statement has become effective under the Securities Act, will be validly issued, fully paid and non-assessable.

We render no opinion herein as to matters involving the laws of any jurisdiction other than New York. This opinion is limited to the effect of the current state of the New York Business Corporation Law (the “NYBCL”) and the facts as they currently exist. We assume no obligation to revise or supplement this opinion in the event of future changes in such law or the interpretations thereof or such facts. We express no opinion regarding any state securities laws or regulations.

Abu Dhabi  •  Beijing  •  Brussels  •  Century City  •  Dallas  •  Denver  •  Dubai  •  Frankfurt  •  Hong Kong  •  Houston  •  London  •  Los Angeles

Munich  •  New York  •  Orange County  •  Palo Alto  •  Paris  •  Riyadh  •  San Francisco  •  Singapore  •  Washington, D.C.

We consent to the filing of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name in the Registration Statement and the prospectus that forms a part thereof. In giving these consents, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations of the Commission.

Very truly yours,

/s/ Gibson, Dunn & Crutcher LLP

Gibson, Dunn & Crutcher LLP