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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-01-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000036270</issuerCik>
        <issuerName>M&amp;T BANK CORP</issuerName>
        <issuerTradingSymbol>MTB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001412211</rptOwnerCik>
            <rptOwnerName>Gold Richard S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE M&amp;T PLAZA</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>BUFFALO</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>14203</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Executive Vice President</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2012-01-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4766</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                    <footnoteId id="F1"/>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>33595.113</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1.868</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F4"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Son</value>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The reported transaction involves an award of restricted stock units under the M&amp;T Bank Corporation 2009 Equity Incentive Compensation Plan. Each restricted stock unit represents a contingent right to receive one share of M&amp;T Bank Corporation common stock upon vesting.</footnote>
        <footnote id="F2">The restricted stock unit award includes a total of 4,766 shares. 1,429 shares of the restricted stock unit award will vest on January 31, 2014; an additional 1,430 shares will vest on January 30, 2015; and the remaining 1,907 shares will vest on January 29, 2016. The resulting shares of common stock received upon settlement will be subject to the restrictions on transfer included in the TARP Interim Final Rule's definition of &quot;long-term restricted stock&quot; until M&amp;T repays the remainder of its TARP obligation.</footnote>
        <footnote id="F3">The restricted stock units were granted under an equity incentive compensation plan maintained by M&amp;T Bank Corporation, and therefore the reporting person paid no price for the restricted stock units.</footnote>
        <footnote id="F4">Jointly owned.</footnote>
        <footnote id="F5">These shares are owned by the son of the reporting person under the Uniform Transfers to Minors Act for which the reporting person is custodian.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By: Brian R. Yoshida, Esq.
(Attorney-in-Fact)</signatureName>
        <signatureDate>2012-02-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
