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Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
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MIC-Info: RSA-MD5,RSA,
 HZb6+yymWH8lLcle3CEQx8r4tu9TuTSkLz7+/HKapwz0IBA6ym51F9PVSVDoZnfn
 zTjb1XXXNM72slYvssaPOw==

<SEC-DOCUMENT>0001179110-06-009940.txt : 20060504
<SEC-HEADER>0001179110-06-009940.hdr.sgml : 20060504
<ACCEPTANCE-DATETIME>20060504130914
ACCESSION NUMBER:		0001179110-06-009940
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20060502
FILED AS OF DATE:		20060504
DATE AS OF CHANGE:		20060504

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			BEMIS CO INC
		CENTRAL INDEX KEY:			0000011199
		STANDARD INDUSTRIAL CLASSIFICATION:	CONVERTED PAPER & PAPERBOARD PRODS (NO CONTAINERS/BOXES) [2670]
		IRS NUMBER:				430178130
		STATE OF INCORPORATION:			MO
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		222 S 9TH ST STE 2300
		CITY:			MINNEAPOLIS
		STATE:			MN
		ZIP:			55402-4099
		BUSINESS PHONE:		6123763000

	MAIL ADDRESS:	
		STREET 2:		222 S 9TH STREET SUITE 2300
		CITY:			MINNEAPOLIS
		STATE:			MN
		ZIP:			55402-4099

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			BOLLINGER JOHN G
		CENTRAL INDEX KEY:			0001215463

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-05277
		FILM NUMBER:		06807244

	BUSINESS ADDRESS:	
		BUSINESS PHONE:		6123763000

	MAIL ADDRESS:	
		STREET 1:		C/O BEMIS CO INC
		STREET 2:		222 S. 9TH ST. #2300
		CITY:			MINNEAPOLIS
		STATE:			MN
		ZIP:			55402
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>edgar.xml
<DESCRIPTION>FORM 4 -
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2006-05-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001215463</rptOwnerCik>
            <rptOwnerName>BOLLINGER JOHN G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>SUITE 2300</rptOwnerStreet1>
            <rptOwnerStreet2>222 S. 9TH ST.</rptOwnerStreet2>
            <rptOwnerCity>MINNEAPOLIS</rptOwnerCity>
            <rptOwnerState>MN</rptOwnerState>
            <rptOwnerZipCode>55402-4099</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>2006-05-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1968</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>31.39</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13968</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2003-05-02</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2006-05-02</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1968</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2006-05-02</value>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2006-05-02</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1968</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Stock Award granted pursuant to Bemis Director's Stock Incentive Plan exempt under Rule 16b-3: Grant to Reporting Person of right to receive stock as of May 2, 2006.  Payout of 1,968 shares was made on May 2, 2006.</footnote>
        <footnote id="F2">Security converts to Common Stock on a one-for-one basis on date of conversion.</footnote>
        <footnote id="F3">Will know price on the date of conversion.</footnote>
    </footnotes>

    <remarks>Reporting Person retired as a Director on May 4, 2006.</remarks>

    <ownerSignature>
        <signatureName>J J Seifert Power of Attorney</signatureName>
        <signatureDate>2006-05-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
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