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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3/A</documentType>

    <periodOfReport>2016-02-17</periodOfReport>

    <dateOfOriginalSubmission>2016-02-26</dateOfOriginalSubmission>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000089800</issuerCik>
        <issuerName>SHERWIN WILLIAMS CO</issuerName>
        <issuerTradingSymbol>SHW</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001666161</rptOwnerCik>
            <rptOwnerName>Baxter Joel D.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>101 W. PROSPECT AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CLEVELAND</rptOwnerCity>
            <rptOwnerState>OH</rptOwnerState>
            <rptOwnerZipCode>44115</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Pres. &amp; GM, Glob. Supply Chain</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7257</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">1,763 shares owned directly by the reporting person were inadvertently omitted from the reporting person's original Form 3 due to an administrative error, and such administrative error carried forward in the reporting person's subsequent Forms 4. Of shares listed, 3,250 are restricted stock and 725 are restricted stock units.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Stephen J. Perisutti, Attorney-in-fact</signatureName>
        <signatureDate>2018-01-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
