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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-03-29</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001245776</rptOwnerCik>
            <rptOwnerName>KING RICHARD G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>900 HIGH STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>HANOVER</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>17331-1639</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-03-29</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>202</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>103.16</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17988</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Phantom Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3231</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This transaction represents stock received by the reporting person in lieu of cash fees pursuant to the M&amp;T Bank Corporation 2008 Directors' Stock Plan.</footnote>
        <footnote id="F2">The reported phantom stock units resulted from the conversion of existing phantom stock units received by the reporting person under a director fee plan maintained by Keystone Financial, Inc., which was acquired by M&amp;T Bank Corporation on October 6, 2000, and represent a like number of shares of M&amp;T Bank Corporation common stock.  The phantom stock units may be settled in shares of M&amp;T Bank Corporation common stock or cash upon a distribution in accordance with the terms of the plan.  The reported phantom stock units also include units acquired through the reporting person's participation in the dividend reinvestment feature of the plan.</footnote>
        <footnote id="F3">The information reported is as of March 31, 2013.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By: Andrea R. Kozlowski, Esq.
(Attorney-In-Fact)</signatureName>
        <signatureDate>2013-04-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
