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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-01-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000011199</issuerCik>
        <issuerName>BEMIS CO INC</issuerName>
        <issuerTradingSymbol>BMS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001286873</rptOwnerCik>
            <rptOwnerName>PEERCY PAUL S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE NEENAH CENTER, 4TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2>P.O. BOX 669</rptOwnerStreet2>
            <rptOwnerCity>NEENAH</rptOwnerCity>
            <rptOwnerState>WI</rptOwnerState>
            <rptOwnerZipCode>54957</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>2012-01-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3149</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>29.78</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21042</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">In addition to the payout of shares in lieu of the annual cash retainer for service in 2011, this amount includes shares received in lieu of the cash retainer for the first quarter of fiscal 2012 in connection with the shift to quarterly, rather than annual, payouts of the annual retainer commencing in 2012.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>Sheri H. Edison Power of Attorney</signatureName>
        <signatureDate>2012-01-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
