<SEC-DOCUMENT>0000030625-23-000059.txt : 20230223
<SEC-HEADER>0000030625-23-000059.hdr.sgml : 20230223
<ACCEPTANCE-DATETIME>20230223170302
ACCESSION NUMBER:		0000030625-23-000059
CONFORMED SUBMISSION TYPE:	4/A
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20230216
FILED AS OF DATE:		20230223
DATE AS OF CHANGE:		20230223

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Gillespie Keith E.
		CENTRAL INDEX KEY:			0001641570

	FILING VALUES:
		FORM TYPE:		4/A
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-13179
		FILM NUMBER:		23660750

	MAIL ADDRESS:	
		STREET 1:		5215 NORTH O'CONNOR BLVD #2300
		CITY:			IRVING
		STATE:			TX
		ZIP:			75039

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			FLOWSERVE CORP
		CENTRAL INDEX KEY:			0000030625
		STANDARD INDUSTRIAL CLASSIFICATION:	PUMPS & PUMPING EQUIPMENT [3561]
		IRS NUMBER:				310267900
		STATE OF INCORPORATION:			NY
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		5215 N. O'CONNOR BLVD.
		STREET 2:		SUITE 700
		CITY:			IRVING
		STATE:			TX
		ZIP:			75039
		BUSINESS PHONE:		9724436500

	MAIL ADDRESS:	
		STREET 1:		5215 N. O'CONNOR BLVD.
		STREET 2:		SUITE 700
		CITY:			IRVING
		STATE:			TX
		ZIP:			75039

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	DURCO INTERNATIONAL INC
		DATE OF NAME CHANGE:	19970508

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	DURIRON CO INC
		DATE OF NAME CHANGE:	19920703

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	THE DURIRON CO INC
		DATE OF NAME CHANGE:	19900509
</SEC-HEADER>
<DOCUMENT>
<TYPE>4/A
<SEQUENCE>1
<FILENAME>wf-form4a_167718976366503.xml
<DESCRIPTION>FORM 4/A
<TEXT>
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    <periodOfReport>2023-02-16</periodOfReport>

    <dateOfOriginalSubmission>2023-02-21</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
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        <issuerName>FLOWSERVE CORP</issuerName>
        <issuerTradingSymbol>FLS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001641570</rptOwnerCik>
            <rptOwnerName>Gillespie Keith E.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>5215 NORTH O'CONNOR BLVD</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 700</rptOwnerStreet2>
            <rptOwnerCity>IRVING</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75039</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP, Chief Sales Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
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                <value>Common Stock</value>
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            <transactionAmounts>
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                <transactionPricePerShare>
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        </nonDerivativeTransaction>
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                <value>Common Stock</value>
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            <transactionDate>
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            <transactionAmounts>
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                    <value>2787</value>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-02-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
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                </sharesOwnedFollowingTransaction>
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            </ownershipNature>
        </nonDerivativeTransaction>
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    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
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            <transactionDate>
                <value>2023-02-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2653</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
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            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2653.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18814</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
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        </derivativeTransaction>
        <derivativeTransaction>
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            <conversionOrExercisePrice>
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            <transactionDate>
                <value>2023-02-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2653</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2653.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>16161</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Rights</value>
            </securityTitle>
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            <transactionDate>
                <value>2023-02-16</value>
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                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>6310</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <footnoteId id="F1"/>
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                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6310.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17131</value>
                </sharesOwnedFollowingTransaction>
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        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each performance right represented a contingent right to receive one share of the issuer's common stock at vesting. The performance rights vested at a rate of 16% (plus dividends accrued on the underlying shares) based on two factors during the three-year performance cycle beginning on January 1, 2020 and ending on December 31, 2022, which are: 1) the issuer's total shareholder return (&quot;TSR&quot;) in comparison to the TSR percentile ranking for companies that comprise the compensation peer group over the performance cycle; and 2) the issuer's return on invested capital (&quot;ROIC&quot;) measured against the issuer's targeted ROIC under its operating plan. The performance rights may be settled, at the issuer's discretion, in cash or shares of common stock.</footnote>
        <footnote id="F2">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.</footnote>
        <footnote id="F3">This Form 4 corrects an inadvertent error in the number of restricted stock units originally reported as disposed of by the officer.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Shakeeb U. Mir, attorney-in-fact</signatureName>
        <signatureDate>2023-02-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
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</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
