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| <?xml version="1.0" encoding="windows-1252"?> |
| <ownershipDocument> |
| <schemaVersion> X0306 </schemaVersion> |
| <documentType> 4 </documentType> |
| <periodOfReport> 2020-07-06 </periodOfReport> |
| <notSubjectToSection16> 0 </notSubjectToSection16> |
| <issuer> |
| | <issuerCik> 0000089800 </issuerCik> |
| | <issuerName> SHERWIN WILLIAMS CO </issuerName> |
| | <issuerTradingSymbol> SHW </issuerTradingSymbol> |
| | </issuer> |
| <reportingOwner> |
| | <reportingOwnerId> |
| | | <rptOwnerCik> 0001051402 </rptOwnerCik> |
| | | <rptOwnerName> KROPF SUSAN J </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> 1 </isDirector> |
| | | <isOfficer> 0 </isOfficer> |
| | | <isTenPercentOwner> 0 </isTenPercentOwner> |
| | | <isOther> 0 </isOther> |
| | | </reportingOwnerRelationship> |
| | </reportingOwner> |
| <derivativeTable> |
| | <derivativeTransaction> |
| | | <securityTitle> |
| <value> Phantom Stock Units </value> |
| </securityTitle> |
| | | <conversionOrExercisePrice> |
| <footnoteId id="F1"/> |
| </conversionOrExercisePrice> |
| | | <transactionDate> |
| <value> 2020-07-06 </value> |
| </transactionDate> |
| | | <deemedExecutionDate></deemedExecutionDate> |
| | | <transactionCoding> |
| <transactionFormType> 4 </transactionFormType> |
| <transactionCode> A </transactionCode> |
| <equitySwapInvolved> 0 </equitySwapInvolved> |
| </transactionCoding> |
| | | <transactionTimeliness> |
| <value></value> |
| </transactionTimeliness> |
| | | <transactionAmounts> |
| <transactionShares> |
| <value> 62.9 </value> |
| <footnoteId id="F1"/> |
| </transactionShares> |
| <transactionPricePerShare> |
| <value> 588.25 </value> |
| </transactionPricePerShare> |
| <transactionAcquiredDisposedCode> |
| <value> A </value> |
| </transactionAcquiredDisposedCode> |
| </transactionAmounts> |
| | | <exerciseDate> |
| <footnoteId id="F1"/> |
| </exerciseDate> |
| | | <expirationDate> |
| <footnoteId id="F1"/> |
| </expirationDate> |
| | | <underlyingSecurity> |
| <underlyingSecurityTitle> |
| <value> Common Stock </value> |
| </underlyingSecurityTitle> |
| <underlyingSecurityShares> |
| <value> 62.9 </value> |
| </underlyingSecurityShares> |
| </underlyingSecurity> |
| | | <postTransactionAmounts> |
| <sharesOwnedFollowingTransaction> |
| <value> 18144.43 </value> |
| <footnoteId id="F2"/> |
| </sharesOwnedFollowingTransaction> |
| </postTransactionAmounts> |
| | | <ownershipNature> |
| <directOrIndirectOwnership> |
| <value> D </value> |
| </directOrIndirectOwnership> |
| </ownershipNature> |
| | | </derivativeTransaction> |
| | </derivativeTable> |
| <footnotes> |
| | <footnote id="F1"> Represents the number of phantom stock units acquired by the reporting person (in an exempt transaction) under the 2005 Director Deferred Fee Plan. Each phantom stock unit is the economic equivalent of one share of common stock. The phantom stock units become payable solely in cash generally upon the reporting person's retirement. </footnote> |
| | <footnote id="F2"> Includes phantom stock units acquired pursuant to the dividend reinvestment feature of the plan. </footnote> |
| | </footnotes> |
| <remarks></remarks> |
| <ownerSignature> |
| | <signatureName> Stephen J. Perisutti, Attorney-in-fact </signatureName> |
| | <signatureDate> 2020-07-08 </signatureDate> |
| | </ownerSignature> |
| </ownershipDocument> |
