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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2018-05-02</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001739321</rptOwnerCik>
            <rptOwnerName>Stephan Louis Fred</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2301 INDUSTRIAL DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEENAH</rptOwnerCity>
            <rptOwnerState>WI</rptOwnerState>
            <rptOwnerZipCode>54956</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President Bemis North America</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2017-02-21</value>
            </exerciseDate>
            <expirationDate>
                <value>2018-12-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>23700</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2017-02-21</value>
            </exerciseDate>
            <expirationDate>
                <value>2019-12-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4575</value>
                    <footnoteId id="F3"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Performance Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2017-02-21</value>
            </exerciseDate>
            <expirationDate>
                <value>2019-12-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10673</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2018-01-02</value>
            </exerciseDate>
            <expirationDate>
                <value>2020-12-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4761</value>
                    <footnoteId id="F5"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Performance Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2018-01-02</value>
            </exerciseDate>
            <expirationDate>
                <value>2020-12-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>11109</value>
                    <footnoteId id="F6"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each unit represents a right to receive one share of Bemis Common Stock upon vesting.</footnote>
        <footnote id="F2">Grant of Restricted Stock Unit exempt under Rule 16b-3. The units will vest on December 31, 2018 and will be settled in the form of Bemis Common Stock as soon as administratively possible thereafter.</footnote>
        <footnote id="F3">Grant of Restricted Stock Unit exempt under Rule 16b-3. The units will vest on December 31, 2019 and will be settled in the form of Bemis Common Stock as soon as administratively possible thereafter.</footnote>
        <footnote id="F4">Grant of Performance Based Restricted Stock Unit exempt under Rule 16b-3. The units will be settled in the form of Bemis Common Stock if certain performance targets are achieved for the performance period ending December 31, 2019. Settlement is expected to occur following Compensation Committee certification of the performance targets, which is anticipated to occur in February 2020.</footnote>
        <footnote id="F5">Grant of Restricted Stock Unit exempt under Rule 16b-3. The units will vest on December 31, 2020 and will be settled in the form of Bemis Common Stock as soon as administratively possible thereafter.</footnote>
        <footnote id="F6">Grant of Performance Based Restricted Stock Unit exempt under Rule 16b-3. The units will be settled in the form of Bemis Common Stock if certain performance targets are achieved for the performance period ending December 31, 2020. Settlement is expected to occur following Compensation Committee certification of the performance targets, which is anticipated to occur in February 2021.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>Sheri H. Edison Power of Attorney</signatureName>
        <signatureDate>2018-05-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
