<SEC-DOCUMENT>0000030625-21-000080.txt : 20210524
<SEC-HEADER>0000030625-21-000080.hdr.sgml : 20210524
<ACCEPTANCE-DATETIME>20210524164212
ACCESSION NUMBER:		0000030625-21-000080
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20210520
FILED AS OF DATE:		20210524
DATE AS OF CHANGE:		20210524

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			DELLY GAYLA J
		CENTRAL INDEX KEY:			0001218358

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-13179
		FILM NUMBER:		21955580

	MAIL ADDRESS:	
		STREET 1:		3000 TECHNOLOGY DR
		CITY:			ANGLETON
		STATE:			TX
		ZIP:			77515

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_162188890777332.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-05-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001218358</rptOwnerCik>
            <rptOwnerName>DELLY GAYLA J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1203 WOODBANK DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>TAYLOR LAKE VILLAGE</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77586</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2021-05-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3587</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>41.81</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8783</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>45981.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>45981</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents the annual restricted stock grant for the director under the Flowserve Long-Term Incentive Plan. The shares vest on May 20, 2022.</footnote>
        <footnote id="F2">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="F3">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/ Akshar C. Patel, attorney-in-fact</signatureName>
        <signatureDate>2021-05-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
