Exhibit 8.1

As of May 2, 2016

Randolph Bancorp

10 Cabot Place

Stoughton, Massachusetts 02072

Ladies and Gentlemen:

You have requested our opinion on certain federal and Massachusetts tax consequences relating to the proposed conversion by Randolph Bancorp (the “MHC”) from a Massachusetts corporation in a mutual holding company structure to a Massachusetts corporation in a stock holding company structure, through a merger with and into its newly-formed wholly-owned subsidiary Randolph Bancorp, Inc. (the “Company”), pursuant to the Plan of Conversion, adopted by the Board of Trustees of the MHC and the Board of Directors of Randolph Savings Bank (the “Bank”) on January 26, 2016, as amended on March 3, 2016 (the “Plan”).¹

For purposes of the opinions set forth below, we have reviewed and relied upon the Plan, the Prospectus of the Company included in the Registration Statement on Form S-1 filed by the Company with the Securities and Exchange Commission, as amended (the “Registration Statement”), and such other documents, records and instruments as we have deemed necessary or appropriate as a basis for our opinions. In addition, in rendering our opinions we have relied upon certain statements, representations and warranties made by the parties to the Conversion (including, without limitation, those contained in certain certified representations and those contained in or made pursuant to the Plan), which we have neither investigated nor verified. We have assumed that such statements, representations and warranties are true, correct, complete and not breached and will continue to be so through the completion of the Conversion, that no actions that are inconsistent with such statements, representations and warranties will be taken, and that all representations, statements, and warranties made “to the best knowledge of” any person(s) or party(ies) or with similar qualification are and will be true, correct and complete as if made without such qualification.

We also have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to the original documents of all documents submitted

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to us as copies, the authority and capacity of the individual or individuals who executed any such documents on behalf of any person, the conformity to the final documents of all documents submitted to us as drafts and the accuracy and completeness of all records made available to us. In addition, we have assumed that the Conversion will be consummated in accordance with the Plan, that each of the parties to the Conversion will comply with all reporting obligations with respect to the Conversion required under the Internal Revenue Code of 1986, as amended (the “Code”), and the Treasury Regulations thereunder, and that the Plan is valid and binding in accordance with its terms.

Any inaccuracy in, or breach of, any of the aforementioned statements, representations, warranties and assumptions or any change after the date hereof in applicable law could adversely affect our opinions. No ruling has been or will be sought from the Internal Revenue Service or any other taxing authority by any party to the Conversion as to the federal income tax consequences of any aspect of the Conversion.

The Bank was chartered as a Massachusetts mutual savings bank in 1851 with all of the powers and privileges, and subject to all the duties, liabilities and restrictions set forth in Massachusetts laws relating to institutions for savings. Pursuant to a reorganization consummated in 2002, the MHC was formed and the Bank converted to stock form and became the wholly-owned subsidiary of the MHC. As a result, the MHC holds all of the Bank’s issued shares of its common stock (“Bank Common Stock”).

On January 26, 2016, the Board of Trustees of the MHC and the Board of Directors of the Bank each adopted the Plan. The Board of Trustees of the MHC and the Board of Directors of the Bank believe that the conversion of the MHC and the Bank into a stock holding company form of organization pursuant to the Plan is in the best interests of the MHC and the Bank, as well as in the best interests of the Bank’s depositors. Accordingly, the following transactions have occurred or will occur in the Conversion pursuant to the Plan:

(1) The MHC has incorporated the Company, a Massachusetts corporation, for the purpose of holding all of the capital stock of the Bank and to facilitate the Conversion.

(2) Subscription rights (“Subscription Rights”) to purchase shares of the common stock of the Company (“Conversion Stock”) have been issued without payment therefor to Eligible Account Holders, Supplemental Eligible Account Holders and Tax-Qualified Employee Plans (as such persons are defined in the Plan). In addition, Subscription Rights have been issued to directors, trustees, Officers, Corporators and Employees of the MHC and the Bank, in a fourth priority category, who do not otherwise qualify as Eligible Account Holders or Supplemental Eligible Account Holders.

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(3) Upon the effective date (the “Effective Date”) of the Conversion, the MHC will merge with and into the Company pursuant to a plan of merger, with the Company being the surviving institution (the “MHC Merger”). As a result of the MHC Merger, (a) the shares of Holding Company Common Stock currently held by the MHC will be extinguished and (b) the Eligible Account Holders and Supplemental Eligible Account Holders will be granted interests in liquidation accounts to be established by the Company and the Bank pursuant to the Plan. Except as otherwise noted, the liquidation account established by the Company and the liquidation account established by the Bank are collectively referred to herein as the “Liquidation Account.”

(4) Upon the Effective Date, the Company will sell shares of Holding Company Conversion Stock in a subscription offering (the “Subscription Offering”) in order of priority to Eligible Account Holders, Supplemental Eligible Account Holders, Tax-Qualified Employee Plans, and directors, trustees, Officers, Corporators and Employees of the MHC and the Bank. Any shares of Holding Company Conversion Stock remaining unsold after the Subscription Offering may be sold to the public through a Direct Community Offering (as defined in the Plan) and a Syndicated Community Offering or a Firm Commitment Underwritten Offering (in each case as defined in the Plan), as determined by the Board of Directors of the Company in its sole discretion. Collectively, the Subscription Offering, the Direct Community Offering and the Syndicated Community Offering and Firm Commitment Underwritten Offering are referred to herein as the “Offerings.”

(5) The Company intends to use approximately $14.0 million of the net proceeds received by the Company in the Offerings for the acquisition for cash of First Eastern Bankshares Corporation and its wholly-owned subsidiary, First Federal Savings Bank of Boston.

The Liquidation Account will be established by the Company and the Bank for the benefit of the Eligible Account Holders and Supplemental Eligible Account Holders who maintain Deposit Accounts (as defined in the Plan) in the Bank after the Conversion. The Liquidation Account balance will initially be an amount equal to the MHC’s net worth as of the date of the latest consolidated statement of financial condition contained in the final Prospectus distributed in connection with the Conversion. Each Eligible Account Holder and Supplemental Eligible Account Holder will have an undivided interest in the Liquidation Account balance (referred to as a “subaccount balance”). The proportionate interest of an Eligible Account Holder or Supplemental Eligible Account Holder in the Liquidation Account will never increase, but will, however, decrease to reflect subsequent withdrawals from the Deposit Account of such Eligible Account Holders or Supplemental Eligible Account Holders. In the sole event of a complete liquidation of the Bank after the Conversion, each Eligible Account Holder and Supplemental Eligible Account Holder will be entitled to receive a liquidation distribution from the Liquidation Account in the amount of their then-current interest before any liquidation

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distribution may be made with respect to the capital stock of the Company. A distribution to an Eligible Account Holder or Supplemental Eligible Account Holder from the liquidation account established by the Company will extinguish the right of such Eligible Account Holder or Supplemental Eligible Account Holder to receive a distribution from the liquidation account established by the Bank.

Each Deposit Account in the Bank at the time of the consummation of the Conversion will become a Deposit Account in the Bank equivalent in withdrawable amount to the withdrawal value (as adjusted to give effect to any withdrawal made for the purchase of Conversion Stock purchased in the Offerings) and subject to the same terms and conditions (except as to liquidation rights) as such Deposit Account in the Bank had immediately preceding consummation of the Conversion.

The following representations have been made by the MHC, the Bank and/or the Company (each, a “Party” and, collectively, the “Parties”) with respect to the Conversion:

(a) The facts relating to the Conversion described in the Plan and the Registration Statement are true, correct, and complete in all material respects. The Plan represents the entire understanding of the MHC, the Bank, and the Company with respect to the Conversion. The Conversion will be consummated in compliance with the terms and conditions of the Plan, and there is no plan or intention to waive or modify any such term or condition.

(b) The aggregate fair market value of the interest in the Liquidation Account and the Subscription Rights received by each Eligible Account Holder or Supplemental Eligible Account Holder pursuant to the MHC Merger will be approximately equal to the fair market value of the equity interest in the MHC surrendered by the Eligible Account Holder or Supplemental Eligible Account Holder in exchange therefor.

(c) To the best of the knowledge of the management of the MHC, the Company, and the Bank, there is no plan or intention on the part of the Eligible Account Holders or Supplemental Eligible Account Holders to withdraw from their Deposit Accounts subsequent to the Conversion such that the withdrawals would reduce their aggregate interests in the Liquidation Account to an amount having a value at the Effective Date of less than forty percent of the value of the aggregate interests which the Eligible Account Holders and Supplemental Eligible Account Holders of the MHC will have in the residual equity of the MHC immediately prior to the Conversion.

(d) The Company has no plan or intention to reacquire any of the interests in the Liquidation Account issued in the MHC Merger.

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(e) The liabilities of the MHC assumed by the Company in the MHC Merger and the liabilities to which the transferred assets of the MHC are subject were incurred by the MHC in the ordinary course of its business.

(f) The Company, the MHC and the Eligible Account Holders and Supplemental Eligible Account Holders will pay their respective expenses, if any, incurred in connection with the Conversion, except that the Company and the MHC may pay fees to brokers and investment bankers for assisting Eligible Account Holders and Supplemental Eligible Account Holders and other eligible subscribers in completing and/or submitting order forms (as defined in the Plan). The expenses for brokers and investment bankers to assist Eligible Account Holders and Supplemental Eligible Account Holders and other eligible subscribers are solely and directly related to the Conversion and will be paid by the Company, the Bank and the MHC directly to the brokers and investment bankers.

(g) There is no intercorporate indebtedness existing between the Company (or any member of the Company’s affiliated group within the meaning of Code Section 1504) and the MHC (or any member of the MHC’s affiliated group within the meaning of Code Section 1504) that was issued, acquired or will be settled at a discount.

(h) None of the Bank, the MHC or the Company is a corporation fifty percent or more of the value of whose total assets are stock and securities and eighty percent or more of the value of whose total assets are held for investment. In making the percentage determinations under the preceding sentence, stock and securities in any subsidiary corporation are disregarded and the parent corporation is deemed to own its ratable share of the subsidiary’s assets, and a corporation is considered a subsidiary if the parent owns fifty percent or more of the combined voting power of all classes of stock entitled to vote or fifty percent or more of the total value of all shares of all classes of stock outstanding.

(i) Neither the MHC nor the Company is under the jurisdiction of a court in a case under title 11 of the United States Code, or under the jurisdiction of a federal or state court in a receivership, foreclosure, or similar proceeding.

(j) The fair market value of the assets of the MHC transferred to the Company in the MHC Merger will, as of the Effective Time, equal or exceed the sum of the liabilities assumed by the Company plus the amount of liabilities, if any, to which the transferred assets are subject.

(k) The Bank has no plan or intention to issue additional shares of its stock that would result in the Company owning less than all of the outstanding stock of the Bank.

(l) The Company has no plan or intention to liquidate the Bank; to merge the Bank with and into another corporation; to sell or otherwise dispose of the stock of the Bank except for

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transfers of stock to corporations controlled by the Company; or to cause the Bank to sell or otherwise dispose of any of its assets, except for dispositions made in the ordinary course of business or transfers of assets to a corporation controlled by the Bank.

(m) On the Effective Date, the fair market value of the assets of the MHC will exceed the sum of its liabilities, plus the amount of liabilities, if any, to which the assets are subject.

(n) The MHC Merger serves genuine and legitimate corporate business purposes which collectively are the principal motivation for the MHC Merger.

(o) Following the MHC Merger, the Company will continue the historic business of the MHC as a bank holding company.

(p) The Company, the Bank and the MHC will report the MHC Merger on their U.S. federal income tax returns as a Code Section 368(a) reorganization and will comply with all reporting obligations relating thereto.

(q) The individual(s) executing the representation letter on behalf of the Bank, the MHC and the Company are authorized to make all of the representations set forth therein on behalf of the Bank, the MHC and the Company, as applicable.

Based upon and subject to the foregoing, as well as the limitations set forth below, it is our opinion with respect to the Conversion that, under present law:

(i) The merger of the MHC with and into the Company, and the issuance of the interests in the Liquidation Account to the Eligible Account Holders and the Supplemental Eligible Account Holders as consideration for the surrender of their equity interests in the MHC, will constitute a “reorganization” under Section 368(a) of the Code. The Company and the MHC each will be a “party to a reorganization” within the meaning of Section 368(b) of the Code.

(ii) The exchange, as a result of the MHC Merger, of the equity interests of the Eligible Account Holders and the Supplemental Eligible Account Holders in the MHC for interests in the Liquidation Account in the MHC Merger will satisfy the continuity of interest requirement of Section 1.368-1(b) of the Income Tax Regulations.

(iii) The MHC will not recognize any income, gain or loss for federal income or Massachusetts corporate excise tax purposes as a result of the MHC Merger or on the transfer of the MHC’s assets to the Company in exchange for an interest in the Liquidation Account for the benefit of the Eligible Account Holders and the Supplemental Eligible Account Holders who remain depositors of the Bank.

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(iv) No income, gain or loss will be recognized by the Company for federal income or Massachusetts corporate excise tax purposes as a result of the MHC Merger or upon the receipt of the assets of the MHC in the MHC Merger in exchange for the transfer to the Eligible Account Holders and the Supplemental Eligible Account Holders of an interest in the Liquidation Account.

(v) For federal income and Massachusetts corporate excise tax purposes, the basis of the assets of the MHC to be received by the Company will be the same as the basis of such assets in the hands of the MHC immediately prior to the transfer.

(vi) For federal income and Massachusetts corporate excise tax purposes, the holding period of the assets of the MHC to be received by the Company will include the holding period of those assets in the hands of the MHC.

(vii) The Eligible Account Holders and Supplemental Eligible Account Holders will recognize no income, gain or loss for federal income or Massachusetts corporate excise or personal income tax purposes as a result of the MHC Merger or upon the receipt of interests in the Liquidation Account in exchange for their liquidation interests in the MHC.

(viii) The Company will recognize no income, gain or loss for federal income or Massachusetts corporate excise tax purposes upon the receipt of cash in the Offerings in exchange for shares of Conversion Stock.

(ix) The Company will recognize no income, gain or loss for federal income or Massachusetts corporate excise tax purposes upon the transfer of a portion of the net proceeds received by the Company in the Offerings to the Bank.

(x) The Bank will recognize no income, gain or loss for federal income or Massachusetts corporate excise tax purposes upon the receipt of the contributed offering proceeds from the Company.

(xi) No income, gain or loss will be recognized by the Company for federal income or Massachusetts corporate excise tax purposes as a result of the distribution to the Eligible Account Holders and Supplemental Eligible Account Holders and such other persons of Subscription Rights relating to Conversion Stock.

(xii) No income, gain or loss will be recognized for federal income or Massachusetts corporate excise or personal income tax purposes by the Eligible Account Holders or

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Supplemental Eligible Account Holders and other persons described in the Plan who received Subscription Rights as a result of the distribution to the Eligible Account Holders and Supplemental Eligible Account Holders and such other persons of Subscription Rights relating to Conversion Stock, provided the Subscription Rights had no value at the time of receipt. Eligible Account Holders and Supplemental Eligible Account Holders and other recipients of Subscription Rights will not recognize income, gain or loss for federal income or Massachusetts corporate excise or personal income tax purposes as a result of the exercise of such Subscription Rights to purchase shares of Conversion Stock, provided that the amount to be paid for the Conversion Stock is equal to the fair market value of the Company’s common stock. The basis of the Conversion Stock to the Company’s stockholders will be the purchase price thereof plus the basis, if any, of the Subscription Rights.

Under past rulings of the Internal Revenue Service (the “IRS”), gain may be recognized by a recipient of Subscription Rights to the extent of the fair market value of the Subscription Rights received. Whether the Subscription Rights have a market value for federal income tax purposes is a question of fact, depending upon all relevant facts and circumstances. The IRS will not issue rulings on whether subscription rights have a market value. However, we are unaware of any instance in which the IRS has taken the position that nontransferable subscription rights issued by a converting financial institution have a market value. We express no opinion on the fair market value of the Subscription Rights.

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We express no opinion herein other than the opinions expressly set forth above. In particular, no opinion is expressed as to the tax consequences of any of the transactions under any foreign, state (other than Massachusetts), or local tax law, or as to the qualification of the Company as a security corporation for Massachusetts tax purposes. You should recognize that our opinions are not binding on the IRS or on the Massachusetts Department of Revenue (“DOR”) and that a court or the IRS or the DOR may disagree with the opinions contained herein. Although we believe that our opinions will be sustained if challenged, there can be no assurance that this will be the case. The discussion and conclusions set forth above are based upon current provisions of the Code, the Income Tax Regulations and Procedure and Administration Regulations promulgated thereunder, the Massachusetts General Laws, the regulations promulgated thereunder, and existing administrative and judicial interpretations thereof (collectively, “Applicable Law”), all of which are subject to change, potentially with retroactive effect. Changes in Applicable Law could adversely affect our opinions. We do not undertake to advise you as to any changes after the date hereof in Applicable Law that may affect our opinions.

This opinion letter is being provided to you in connection with the filing of the Registration Statement. This opinion letter may be used by the Massachusetts Division of Banks

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and the Board of Governors of the Federal Reserve System as part of their review and approval of the Conversion. We hereby consent to the inclusion of this opinion as Exhibit 8.1 to the Registration Statement and to the references to our firm under the caption “Legal and Tax Matters” in the Registration Statement. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations thereunder.