<SEC-DOCUMENT>0000030625-22-000090.txt : 20221213
<SEC-HEADER>0000030625-22-000090.hdr.sgml : 20221213
<ACCEPTANCE-DATETIME>20221213175522
ACCESSION NUMBER:		0000030625-22-000090
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20221213
FILED AS OF DATE:		20221213
DATE AS OF CHANGE:		20221213

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			SIEGEL KENNETH I
		CENTRAL INDEX KEY:			0001465558

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-13179
		FILM NUMBER:		221460648

	MAIL ADDRESS:	
		STREET 1:		667 MADISON AVENUE
		CITY:			NEW YORK
		STATE:			NY
		ZIP:			10065

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_167097210678349.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-12-13</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001465558</rptOwnerCik>
            <rptOwnerName>SIEGEL KENNETH I</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>5215 N O CONNOR BLVD</rptOwnerStreet1>
            <rptOwnerStreet2># 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>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-12-13</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3229</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3229</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents the pro-rata annual restricted stock grant for the director under the Flowserve Long-Term Incentive Plan. The shares vest on May 12, 2023.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Shakeeb U. Mir, attorney-in-fact</signatureName>
        <signatureDate>2022-12-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
