Exhibit 5.1

[WLRK LETTERHEAD]

February 11, 2014

M&T Bank Corporation

One M&T Plaza

Buffalo, New York 14203

Ladies and Gentlemen:

We have acted as special counsel to M&T Bank Corporation (the “Company”), a New York corporation, in connection with the offer and sale (the “Offering”) by the Company of 350,000 shares of the Company’s Perpetual Fixed-to-Floating Rate Non-Cumulative Preferred Stock, Series E, liquidation preference $1,000 per share (the “Preferred Shares”), pursuant to the Underwriting Agreement (the “Underwriting Agreement”), dated February 6, 2014, by and among the Company and J.P. Morgan Securities LLC, Citigroup Global Markets Inc. and Credit Suisse Securities (USA) LLC as representatives of the several underwriters listed on Schedule A attached thereto (the “Underwriters”). The Preferred Shares are being offered and sold under a registration statement on Form S-3ASR under the Securities Act of 1933, as amended (the “Securities Act”), filed with the Securities and Exchange Commission (the “Commission”) on June 26, 2012 (File No. 333-182348) (the “Registration Statement”), including a base prospectus dated June 26, 2012, and a prospectus supplement dated February 6, 2014 (the “Prospectus Supplement”).

In rendering this opinion to the Company, we have examined such corporate records and other documents, and we have reviewed such matters of law, as we have deemed necessary or appropriate. In rendering this opinion, we have, with your consent, relied upon oral and written representations of officers of the Company and certificates of officers of the Company and public officials with respect to the accuracy of the factual matters addressed in such representations and certificates. In addition, in rendering this opinion we have, with your consent, assumed the genuineness of all signatures or instruments relied upon by us, and the conformity of certified copies submitted to us with the original documents to which such certificates copies relate.

Based on the foregoing, and subject to the qualifications and limitations stated herein, we are of the opinion that the Preferred Shares have been duly authorized and, upon payment and delivery in accordance with the Underwriting Agreement, the Preferred Shares will be validly issued, fully paid and non-assessable.

The opinion set forth above is subject to the effects of (a) bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting the enforcement of creditors’ rights generally, (b) general equitable principles (whether

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considered in a proceeding in equity or at law) and (c) an implied covenant of good faith and fair dealing. We express no opinion as to whether, or the extent to which, the laws of any particular jurisdiction apply to the subject matter hereof, including, without limitation, the enforceability of the governing law provision contained in the Underwriting Agreement.

This opinion is given on the basis of the statutory laws and judicial decisions in effect, and the facts existing, as of the date hereof. We have not undertaken any obligation to advise you of changes in matters of fact or law which may occur, and we do not opine with respect to any law, regulation, rule or governmental policy which may be enacted or adopted, after the date hereof.

We are members of the Bar of the State of New York, and we have not considered, and we express no opinion as to, the laws of any jurisdiction other than the laws of the State of New York and the federal laws of the United States of America, in each case as in effect on the date hereof.

We hereby consent to the filing of this opinion with the Commission as an Exhibit to the Company’s Current Report on Form 8-K dated February 11, 2014. We also consent to the reference to our firm under the caption “Legal Matters” in the Prospectus Supplement constituting a part of the Registration Statement. In giving this consent, we do not thereby admit that we are experts within the meaning of Section 11 of the Securities Act or included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

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Very truly yours,

/s/ Wachtell, Lipton, Rosen & Katz