Exhibit 5.1

April 10, 2019

Flowserve Corporation

5215 N. O’Connor Boulevard, Suite 2300

Irving, Texas 75039

Ladies and Gentlemen:

We have acted as securities counsel for Flowserve Corporation, a New York corporation (the “Company”), in connection with its filing with the Securities and Exchange Commission (the “SEC”) of a registration statement on Form S-3 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”), with respect to the offer and sale from time to time, pursuant to Rule 415 of the General Rules and Regulations promulgated under the Securities Act, of the following securities with an indeterminate aggregate initial public offering price: (i) shares of common stock, $1.25 par value per share, of the Company (the “Common Stock”), (ii) shares of preferred stock, $1.00 par value per share, of the Company (the “Preferred Stock”), and (iii) debt securities of the Company, which may be issued in one or more series (the “Notes” and together with the Common Stock and the Preferred Stock, the “Offered Securities”).

We have reviewed executed copies of that certain Senior Indenture, dated September 11, 2012, between the Company and U.S. Bank National Association, as trustee (the “Trustee”), as supplemented by the First Supplemental Indenture, dated September 11, 2012, by and among the Company and the Trustee, the Second Supplemental Indenture, dated November 1, 2013, by and among the Company and the Trustee and the Third Supplemental Indenture, dated March 17, 2015, by and among the Company and the Trustee (as supplemented, the “Indenture”), and we have examined the originals, or photostatic or certified copies, of such records of the Company, of certificates of officers of the Company and of public documents, and such other documents as we have deemed relevant and necessary as the basis of the opinions set forth below.

In rendering the opinions set forth below, we have assumed that (i) all information contained in all documents reviewed by us is true and correct, (ii) all signatures on all documents examined by us are genuine, (iii) all documents submitted to us as originals are authentic and all documents submitted to us as copies conform to the originals of those documents, (iv) each natural person signing any document reviewed by us had the legal capacity to do so, (v) each person signing in a representative capacity (other than on behalf of the Company) any document reviewed by us had authority to sign in such capacity, (vi) the Registration Statement, and any amendments thereto (including any post-effective amendments), will have become effective and comply with all applicable laws and such effectiveness shall not have been terminated or rescinded, (vii) a prospectus supplement will have been prepared and timely filed with the SEC describing the Offered Securities, (viii) all Offered Securities will be issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement and the applicable prospectus supplement, (ix) any supplemental indenture relating to a series of Notes to be issued under the Indentures will be duly authorized, executed and delivered by the parties thereto in substantially the form reviewed by us, (x) with respect to Notes, the trustee shall have been qualified under the Trust Indenture Act of 1939, as amended, and a Statement of Eligibility of the Trustee on a Form T-1 will be filed with the SEC with respect to such trustee, (xi) if in an underwritten offering, a definitive purchase, underwriting or similar agreement with respect to any Offered Securities will be duly authorized and validly executed and delivered by the Company and the other parties thereto, (xii) any Offered Securities issuable upon conversion, exchange or exercise of any Offered Security will be duly authorized, created and, if appropriate, reserved for issuance upon such conversion, exchange or exercise,

and (xiii) with respect to Common Stock or Preferred Stock offered (including upon exercise, conversion or exchange of any Notes), there will be sufficient Common Stock or Preferred Stock authorized under the Company’s Restated Certificate of Incorporation and By-Laws and not otherwise reserved for issuance.

Based upon and subject to the foregoing, we are of the opinion that:

1. Upon (a) due adoption by the board of directors of the Company of a resolution duly authorizing the issuance and delivery of Common Stock in form and content as required by applicable law, (b) due execution and delivery of an enforceable underwriting agreement by each of the parties thereto and (c) issuance and delivery of, and payment for, such shares in the manner contemplated in the Registration Statement and the related prospectus supplement and by such resolution, such shares of Common Stock that may be offered and sold by the Company (including any Common Stock duly issued (i) upon the exchange or conversion of Notes that are exchangeable or convertible into Common Stock or (ii) upon the exchange or conversion of any shares of Preferred Stock that are exchangeable or convertible into Common Stock) will be validly issued, fully paid and non-assessable.

2. Upon (a) due adoption by the board of directors of the Company of a resolution to duly establish a series of Preferred Stock in accordance with the terms of the Restated Certificate of Incorporation of the Company and applicable law, (b) filing by the Company of a certificate of designations with the Secretary of State of the State of New York in accordance with and as required by applicable law, (c) due adoption by the board of directors of the Company of a resolution duly authorizing the issuance and delivery of Preferred Stock in form and content as required by applicable law, (d) due execution and delivery of an enforceable underwriting agreement by the parties thereto and (e) issuance and delivery of, and payment for, such shares in the manner contemplated by the Registration Statement, the related prospectus supplement and such resolutions, such shares of such series of Preferred Stock (including any Preferred Stock duly issued upon the exchange or conversion of Notes that are exchangeable or convertible into Preferred Stock) will be validly issued, fully paid and non-assessable.

3. When (a) the board of directors of the Company has duly adopted a resolution authorizing the execution, delivery, and performance of the supplement to the Indenture for a particular issuance of Notes (the “Indenture Supplement”), (b) the Notes have been duly established in conformity with the Indenture Supplement (including, without limitation, the adoption by the board of directors of the Company of a resolution duly authorizing the issuance and delivery of the Notes in form and content as required by applicable law) and duly authenticated by the Trustee, (c) the Indenture Supplement has been duly executed and delivered by the Company and the Trustee becoming enforceable obligations of the parties thereto, (d) due execution and delivery of an enforceable underwriting agreement by the parties thereto and (e) such Notes have been duly executed and delivered against payment therefor in accordance with the Indenture and Indenture Supplement and issued and sold as contemplated in the Registration Statement and the related prospectus supplement, the Notes will constitute binding obligations of the Company.

The opinions expressed above are limited to the laws of the State of New York and the federal laws of the United States of America.

This opinion letter is limited to the matters stated herein, and no opinion is implied or may be inferred beyond the matters expressly stated. We hereby consent to the use of our opinion as herein set forth as an exhibit to the Registration Statement and to the use of our name under the caption “Legal Matters” in the prospectus forming a part of the Registration Statement. In giving this consent, we do not hereby admit that we come within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the SEC promulgated thereunder or Item 509 of Regulation S-K.

Very truly yours,

/s/ Baker & McKenzie LLP

BAKER & McKENZIE LLP