<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0407</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-05-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000099780</issuerCik>
        <issuerName>TRINITY INDUSTRIES INC</issuerName>
        <issuerTradingSymbol>NYSE/TRN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001775725</rptOwnerCik>
            <rptOwnerName>MACLIN TODD</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>14221 N. DALLAS PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1100</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75254</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Trinity Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-05-08</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6473</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6473.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6473</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Restricted Stock Units granted pursuant to the Fifth Amended and Restated Trinity Industries, Inc. 2004 Stock Option and Incentive Plan. Distribution is 1 for 1 in Trinity Stock after Director's termination. Units vest upon the first annual stockholders meeting following the Date of Grant.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Christina Maldonado for: Todd Maclin</signatureName>
        <signatureDate>2023-05-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0407
4
2023-05-08
0
0000099780
TRINITY INDUSTRIES INC
NYSE/TRN
0001775725
MACLIN TODD
14221 N. DALLAS PARKWAY
SUITE 1100
DALLAS
TX
75254
1
0
0
0
0
Trinity Stock Units
0.0
2023-05-08
4
A
0
6473
0
A
Common Stock
6473.0
6473
D
Restricted Stock Units granted pursuant to the Fifth Amended and Restated Trinity Industries, Inc. 2004 Stock Option and Incentive Plan. Distribution is 1 for 1 in Trinity Stock after Director's termination. Units vest upon the first annual stockholders meeting following the Date of Grant.
Christina Maldonado for: Todd Maclin
2023-05-10