<SEC-DOCUMENT>0000030625-21-000103.txt : 20211104
<SEC-HEADER>0000030625-21-000103.hdr.sgml : 20211104
<ACCEPTANCE-DATETIME>20211104162221
ACCESSION NUMBER:		0000030625-21-000103
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20211102
FILED AS OF DATE:		20211104
DATE AS OF CHANGE:		20211104

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Taylor Carlyn R.
		CENTRAL INDEX KEY:			0001821412

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-13179
		FILM NUMBER:		211380368

	MAIL ADDRESS:	
		STREET 1:		5215 N. O'CONNOR BLVD.
		STREET 2:		SUITE 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
<SEQUENCE>1
<FILENAME>wf-form4_163605732368239.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-11-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000030625</issuerCik>
        <issuerName>FLOWSERVE CORP</issuerName>
        <issuerTradingSymbol>FLS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001821412</rptOwnerCik>
            <rptOwnerName>Taylor Carlyn R.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>5215 N. O'CONNOR BLVD.</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 700</rptOwnerStreet2>
            <rptOwnerCity>IRVING</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75039</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2021-11-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>850</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.85</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>850.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6604</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each share of phantom stock is the economic equivalent of one share of common stock, and represents director compensation deferred in the form of common stock pursuant to the issuer's deferred compensation plan.</footnote>
        <footnote id="F2">The shares of phantom stock become payable in the form of common stock upon the reporting person's termination of service as a member of the issuer's board of directors.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Shakeeb U. Mir, attorney-in-fact</signatureName>
        <signatureDate>2021-11-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
