Exhibit 8.1

Covington & Burling LLP One CityCenter 850 Tenth Street, NW Washington, DC 20001-4956 T  +1 202 662 6000

March 9, 2020

Evans Bancorp, Inc.

Evans Bank, N.A.

One Grimsby Drive

Hamburg, NY 14075

Re: Mergers of FSB Bancorp, Inc. with and into Evans Bancorp, Inc.

Ladies and Gentlemen:

We have acted as counsel to Evans Bancorp, Inc., a New York corporation (“Evans”), in connection with the proposed merger of MMS Merger Sub, Inc., a Maryland corporation and wholly owned subsidiary of Evans (“Merger Sub”) with and into FSB Bancorp, Inc., a Maryland corporation (“FSB”), with FSB surviving (the “First Merger”), followed immediately by the merger of FSB with and into Evans, with Evans surviving (the “Second Merger,” and with the First Merger, the “Mergers”), pursuant to the terms of the Agreement and Plan of Reorganization, dated as of December 19, 2019, as amended on March 5, 2020 (the “Agreement”), by and between Evans, Merger Sub, and FSB as described in the Registration Statement on Form S-4 (File No. 333-236425) filed by Evans with the United States Securities and Exchange Commission (as amended to the date hereof, the “Registration Statement”). In connection therewith, we prepared the discussion (the “Discussion”) set forth under the caption “Material U.S. Federal Income Tax Consequences Relating to the Mergers” in the Registration Statement.

In connection with this opinion, we have reviewed (i) the Agreement, (ii) the Registration Statement and (iii) such other records, certificates and other documents, and such questions of law, as we have considered necessary or appropriate for the purposes of this opinion.

We have assumed that all signatures are genuine, that all documents submitted to us as originals are authentic and that all copies of documents submitted to us conform to the originals. We have further assumed, with your permission (to the extent set forth in the representation letters from Evans and FSB) and without independent investigation, that (i) the Mergers will be consummated in the manner described in the Registration Statement and in accordance with the Agreement, (ii) the Mergers will be consummated without the waiver of any conditions to any party’s obligations to consummate the Mergers and (iii) the covenants set forth in the Agreement will be complied with. We have assumed further the accuracy of the representations set forth in the Agreement and in certificates as to certain factual matters signed by officers of Evans and FSB. We have also assumed, with your permission and without independent investigation (other than such investigations as we have deemed necessary to fulfill our professional responsibilities as

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March 9, 2020

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counsel), that, as to all matters in which a person making a representation has represented that such person or a related party is not a party to, does not have, or is not aware of any plan, intention, understanding, or agreement to take action, there is in fact no such plan, intention, understanding, or agreement, and such action will not be taken.

Based upon and subject to the foregoing, we hereby confirm that the legal statements in the Discussion constitute our opinion with respect to the United States federal income tax law matters referred to therein.

Our opinion expressed herein is subject to the assumptions and qualifications set forth in the Discussion and is based upon existing law, regulations, administrative pronouncements and judicial authority, all as in effect as of today’s date. This opinion is not binding on the Internal Revenue Service or courts. Furthermore, the authorities upon which we rely may be changed at any time, potentially with retroactive effect. No assurances can be given as to the effect of any such changes on the conclusions expressed in this opinion. Our opinion is limited to the United States federal income tax matters specifically covered hereby, and we have not been asked to address, nor have we addressed, any other tax consequences. We undertake no responsibility to advise you of any future change in the matters stated or assumed herein or in the United States federal income tax laws or the application or interpretation thereof.

We are furnishing this opinion solely in connection with the filing of the Registration Statement, and this opinion is not to be relied upon for any other purpose. We hereby consent to the filing of this opinion with the United States Securities and Exchange Commission as an exhibit to the Registration Statement and the references to this opinion in the Registration Statement. In giving such consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended.

Very truly yours,

/s/ Covington & Burling LLP

Covington & Burling LLP