EXHIBIT 5.1

November 2, 2015

M&T Bank Corporation

One M&T Plaza

Buffalo, New York 14240

Ladies and Gentlemen:

Reference is made to Post-Effective Amendment No. 1 (the “Amendment”) to Registration Statement on Form S-4 (the “Registration Statement”) of M&T Bank Corporation (the “Corporation”) related to the registration of 1,383,500 shares of the Corporation’s common stock, par value $0.50 per share (“Common Stock”), which, as a result of the merger effective on November 1, 2015 of Hudson City Bancorp, Inc. (“Hudson City”) with and into Wilmington Trust Corporation (“Wilmington Trust”), may be issued by the Corporation under the Hudson City Bancorp, Inc. Amended and Restated 2011 Stock Incentive Plan, the Hudson City Bancorp, Inc. 2006 Stock Incentive Plan and the Profit Incentive Bonus Plan of Hudson City Savings Bank (the “Plans”).

I have been requested to furnish an opinion to be included as Exhibit 5.1 to the Registration Statement. In conjunction with the furnishing of this opinion, I have examined such corporate documents and have made such investigation of matters of fact and law as I have deemed necessary to render this opinion.

This opinion rendered in my capacity as Group Vice President and Deputy General Counsel of the Corporation and is limited to matters governed by the Federal laws of the United States of America and the Business Corporation Law of the State of New York. This opinion speaks as of today’s date, does not address any matters other than those expressly stated herein, and is limited to present statutes, regulations and judicial interpretations. In rendering this opinion, I assume no obligation to revise or supplement this opinion should present laws, regulations or judicial interpretations be changed by legislative or regulatory action, judicial decision or otherwise.

Based upon such examination and investigation, and upon the assumption that there will be no material changes in the documents examined and matters investigated and that at the time of issuance there will be authorized but unissued shares of Common Stock available to the Corporation in sufficient amounts, I am of the opinion that the shares of Common Stock referred to above have been duly authorized by the Corporation and that, when issued in accordance with the terms of the Plans, will be validly issued, fully paid and non-assessable. I consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement, and to the references therein to my name and this opinion. In giving such consent, I do not admit that I am in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Brian R Yoshida

Brian R. Yoshida

Group Vice President and

Deputy General Counsel