<SEC-DOCUMENT>0000030625-22-000032.txt : 20220222
<SEC-HEADER>0000030625-22-000032.hdr.sgml : 20220222
<ACCEPTANCE-DATETIME>20220222174854
ACCESSION NUMBER:		0000030625-22-000032
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20220220
FILED AS OF DATE:		20220222
DATE AS OF CHANGE:		20220222

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Rowe Robert Scott
		CENTRAL INDEX KEY:			0001608962

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-13179
		FILM NUMBER:		22659666

	MAIL ADDRESS:	
		STREET 1:		1333 WEST LOOP SOUTH, SUITE 1700
		CITY:			HOUSTON
		STATE:			TX
		ZIP:			77027

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_164557010058756.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-02-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001608962</rptOwnerCik>
            <rptOwnerName>Rowe Robert Scott</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>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President &amp; CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-02-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>21201</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>245176</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2022-02-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>8343</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>32.06</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>236833</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2022-02-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>20150</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>20150.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>284794</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">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>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Shakeeb U. Mir, attorney-in-fact</signatureName>
        <signatureDate>2022-02-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
