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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-03-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001199503</rptOwnerCik>
            <rptOwnerName>ALLOTT ANTHONY J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>SILGAN HOLDINGS INC.</rptOwnerStreet1>
            <rptOwnerStreet2>4 LANDMARK SQUARE - SUITE 400</rptOwnerStreet2>
            <rptOwnerCity>STAMFORD</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06901</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-03-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>21609</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>28.55</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>953095</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-03-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>44300</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>997395</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">On May 26, 2017, a two-for-one stock split of the Common Stock of Silgan Holdings Inc. in the form of a stock dividend was effected, resulting in the reporting person's direct ownership of 487,352 additional shares of Common Stock of Silgan Holdings Inc. on such date (including 275,780 additional restricted stock units).</footnote>
        <footnote id="F2">These securities are restricted stock units that were granted on March 1, 2018 under the Silgan Holdings Inc. Amended and Restated 2004 Stock Incentive Plan.  These restricted stock units vest ratably over a 5 year period beginning on March 1, 2019 and will be settled in shares of Common Stock on a 1-for-1 basis upon vesting.</footnote>
        <footnote id="F3">This amount includes 548,940 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/ Anthony J. Allott</signatureName>
        <signatureDate>2018-03-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
