<?xml version="1.0"?><ownershipDocument>
    <schemaVersion>X0101</schemaVersion>

    <documentType>4</documentType><periodOfReport>2003-07-01</periodOfReport>
    <issuer>
        <issuerCik>0000036270</issuerCik>
        <issuerName>M&amp;T BANK CORP</issuerName>
        <issuerTradingSymbol>MTB</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId>
            <rptOwnerCik>0001034049</rptOwnerCik>
            <rptOwnerName>NEWMAN REGINALD B II</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>  </rptOwnerStreet1>
            <rptOwnerStreet2>  </rptOwnerStreet2>
            <rptOwnerCity>  </rptOwnerCity>
            <rptOwnerState>  </rptOwnerState>
            <rptOwnerZipCode>  </rptOwnerZipCode>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle></officerTitle><otherText></otherText></reportingOwnerRelationship></reportingOwner><nonDerivativeSecurity><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-07-01</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F1" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>94</value></transactionShares><transactionValue><value>84.22</value></transactionValue><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2951</value><footnoteId id="F2" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value><footnoteId id="F3" /></directOrIndirectOwnership></ownershipNature></nonDerivativeSecurity><footnotes><footnote id="F1">Stock received in lieu of cash fees pursuant to the M&amp;T Bank Corporation Directors' Stock Plan.</footnote><footnote id="F2">The indicated shares include the reporting person's direct and indirect beneficial ownership.  The reported transaction only affected the reporting person's direct beneficial ownership.  Of the indicated shares, 1,721 are held directly and 1,230 are held indireclty.</footnote><footnote id="F3">The 1,230 shares indicated in footnote (2) as being held indirectly are held by wife.  The reporting person disclaims beneficial ownership of these securities, and this report shall not be deemed an admission that the reporting person is the beneficial owner of such securities for the purposes of Section 16 or for any other purpose.</footnote></footnotes><ownerSignature><signatureName>By: Brian R. Yoshida, Esq.
(Attorney-In-Fact)</signatureName><signatureDate>2003-07-02</signatureDate></ownerSignature></ownershipDocument>

