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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-05-22</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000849869</issuerCik>
        <issuerName>SILGAN HOLDINGS INC</issuerName>
        <issuerTradingSymbol>SLGN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001413028</rptOwnerCik>
            <rptOwnerName>Snyder Thomas James</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>SILGAN CONTAINERS LLC</rptOwnerStreet1>
            <rptOwnerStreet2>21600 OXNARD STREET - SUITE 1600</rptOwnerStreet2>
            <rptOwnerCity>WOODLAND HILLS</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>91367</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President - Silgan Containers</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-05-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10464</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>27.5484</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>136880</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The range of sales prices for 05/22/2018 was $27.51 - $27.63.  The reporting person undertakes to provide, upon the request of the SEC staff, the Issuer or any security holder of the Issuer, full information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F2">This amount consists of 136,880 restricted stock units that are not yet vested that have been granted under the Silgan Holdings Inc. Amended and Restated 2004 Stock Incentive Plan.  Upon vesting, these restricted stock units will be settled in shares of Common Stock on a 1-for-1 basis.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Frank W. Hogan, III, Attorney-in-fact for Thomas J. Snyder</signatureName>
        <signatureDate>2018-05-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
