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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-06-11</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001434813</rptOwnerCik>
            <rptOwnerName>NOVO GUILLERMO</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2301 INDUSTRIAL DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEENAH</rptOwnerCity>
            <rptOwnerState>WI</rptOwnerState>
            <rptOwnerZipCode>54956</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>2019-06-11</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3511</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Disposed of as a result of merger pursuant to the previously announced Transaction Agreement, dated as of August 6, 2018 (which, as it may be amended from time to time, we refer to as the &quot;Transaction Agreement&quot;), by and among Amcor plc (f/k/a Arctic Jersey Limited)(&quot;New Amcor&quot;), Amcor Limited, Arctic Corp. and Bemis Company, Inc.</footnote>
        <footnote id="F2">Includes 96 shares acquired pursuant to a dividend equivalent feature upon settlement of a restricted stock unit.</footnote>
        <footnote id="F3">Each share of common stock was cancelled pursuant to the Transaction Agreement in exchange for the right to receive the consideration provided in the Transaction Agreement (i.e., 5.1 ordinary shares of New Amcor for each such share, subject to applicable tax withholding and with cash payable in lieu of any fractional shares).</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>Sheri H. Edison Power of Attorney</signatureName>
        <signatureDate>2019-06-11</signatureDate>
    </ownerSignature>
</ownershipDocument>