Exhibit 5.1

29 July 2020

To: Board of Directors

Alkermes plc

Connaught House

Burlington Road

Dublin 4

Ireland

Re: Alkermes plc - registration statement on Form S-8 in relation to the Alkermes plc 2018 Stock Option and Incentive Plan, as amended, the Amended and Restated 2008 Stock Option and Incentive Plan and the Alkermes plc 2011 Stock Option and Incentive Plan, as amended

Dear Sirs

1. Basis of Opinion

1.1 We are acting as Irish counsel to Alkermes plc, registered number 498284, a public company limited by shares, incorporated under the laws of Ireland, with its registered office at Connaught House, 1 Burlington Road, Dublin 4 (the “Company”), in connection with the Post-Effective Amendment to the original Registration Statements on Form S-8 (Registration Nos. 333-179545, 333-184621, 333-200777, 333-214952, 333-226359) to be filed with the United States Securities and Exchange Commission (the “SEC”) on the date hereof (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”) with respect to (a) the number of ordinary shares with nominal value US$0.01 per share (the “Ordinary Shares”) of the Company that remained available for grant under theAlkermes plc 2011 Stock Option and Incentive Plan, as amended (the “2011 Plan”) as of 20 May 2020 (the “Effective Date”), (which Ordinary Shares ceased to be available for grant under the 2011 Plan as of the Effective Date) and (b) the number of Ordinary Shares underlying any outstanding awards granted under the Amended and Restated 2008 Stock Option and Incentive Plan (the “2008 Plan”) and the 2011 Plan that are forfeited, cancelled, repurchased or otherwise terminated (other than by exercise) after the Effective Date as such Ordinary Shares may become available from time to time (the Ordinary Shares described in (a) and (b) together, the “Shares”), which Shares will become available for issuance under the Alkermes plc 2018 Stock Option and Incentive Plan, as amended (the “2018 Plan”) pursuant to awards granted under the 2018 Plan.

1.2 This Opinion is confined to and given in all respects on the basis of the laws of Ireland (meaning Ireland exclusive of Northern Ireland) in force as at the date hereof as currently applied by the courts of Ireland. We have made no investigation of and we express no opinion as to the laws of any other jurisdiction or the effect thereof. In particular, we express no opinion on the laws of the European Union as they affect any jurisdiction other than Ireland. We have assumed without investigation that insofar as the laws of any jurisdiction other than Ireland are relevant, such laws do not prohibit

and are not inconsistent with any of the obligations or rights expressed in the Plan Documents (as set out in the Schedule) or the transactions contemplated thereby.

1.3 This Opinion is also strictly confined to:

(a) the matters expressly stated herein at paragraph 2 below and is not to be read as extending by implication or otherwise to any other matter;

(b) the Plan Documents (as set out in the Schedule); and

(c) the Searches (as defined at 1.7 below),

and is subject to the assumptions and qualifications set out below.

1.4 We express no opinion, and make no representation or warranty, as to any matter of fact or in respect of any documents which may exist in relation to the 2008 Plan, the 2011 Plan or the 2018 Plan or the Shares other than the Plan Documents.

1.5 In giving this Opinion, we have relied upon the Corporate Certificate (as defined in the Schedule to this Opinion) and the Searches and we give this Opinion expressly on the terms that no further investigation or diligence in respect of any matter referred to in the Corporate Certificate or the Searches is required of us.

1.6 For the purpose of giving this Opinion, we have examined and relied on copies sent to us by email in pdf or other electronic format of the Plan Documents.

1.7 For the purpose of giving this Opinion, we have caused to be made legal searches against the Company on 29 July 2020 (together the “Searches”):

(a) on the file of the Company maintained by the Registrar of Companies in the Irish Companies Registration Office for mortgages, debentures or similar charges or notices thereof and for the appointment of any examiner, receiver or liquidator;

(b) in the Judgments Office of the High Court for unsatisfied judgments, orders, decrees and the like for the five years immediately preceding the date of the search; and

(c) in the Central Office of the High Court for any proceedings and petitions filed in respect of the Company in the last two years.

1.8 This Opinion is governed by and is to be construed in accordance with the laws of Ireland as interpreted by the courts of Ireland at the date hereof. This Opinion speaks only as of its date. We assume no obligation to update this Opinion at any time in the future or to advise you of any change in law or change in interpretation of law which may occur after the date of this Opinion.

2. Opinion

Subject to the assumptions and qualifications set out in this Opinion and to any matters not disclosed to us, we are of the opinion that:

2.1 The Company is a public company limited by shares, is duly incorporated and validly existing under the laws of Ireland and has the requisite corporate authority to allot and issue the Shares.

2.2 When the Shares are allotted and issued (and, if required, paid for in cash) pursuant to and in accordance with the terms and conditions referred to or summarised in the applicable resolutions and the 2018 Plan, the Shares will be validly issued, fully paid up and non-assessable (which term means when used herein that no further sums are required to be paid by the holders thereof in connection with the allotment and issue of such Shares).

3. Assumptions

For the purpose of giving this Opinion, we assume the following without any responsibility on our part if any assumption proves to have been untrue as we have not verified independently any assumption:

The Registration Statement and the 2018 Plan

3.1 that when filed with the SEC, the Registration Statement for the 2018 Plan will not differ in any material respect from the latest draft that we have examined;

3.2 that any awards granted pursuant to the 2018 Plan will be paid up in consideration of the receipt by the Company prior to, or simultaneously with, the allotment and issue of the Shares pursuant thereto of cash at least equal to the nominal value of such Shares and any premium required to be paid up on the Shares pursuant to their terms of allotment and issue and that where Shares are allotted and issued under the 2018 Plan without the requirement for the payment of cash consideration by or on behalf of the relevant beneficiary, then such Shares shall either be fully paid up by the Company or one of its subsidiaries within the time permitted by section 1027(1) of the Companies Act 2014 (as amended) (the “Companies Act”) (and, in the case of the Company or a subsidiary incorporated in Ireland, in a manner permitted by sections 82(6) and 1043(1) of the Companies Act or allotted and issued for consideration as set out in section 1028(2) of the Companies Act);

3.3 that the filing of the Registration Statement with the SEC has been authorised by all necessary actions under all applicable laws (other than Irish law), including applicable U.S. federal and state securities laws;

3.4 that the exercise of any options and rights granted under the 2018 Plan and the allotment and issue of the Shares upon exercise of such options and rights (and the allotment and issue of the Shares in connection with any other awards granted under the 2018 Plan) will be conducted in accordance with the terms and the procedures described in the 2018 Plan and the applicable award agreement;

3.5 that at the time of the allotment and issuance of the Shares, such allotment and issuance shall not be in contravention or breach of any agreement, undertaking, arrangement, deed or covenant affecting the Company or to which the Company is a party or otherwise bound or subject;

3.6 that the Company has sufficient authorised but unissued share capital to allot and issue the required number of Shares to be delivered to the recipients of any awards granted under the 2018 Plan;

3.7 that, at the time of the allotment and issuance of the Shares, the authority of the Company and the directors of the Company to allot and issue the Shares, as provided for in the Companies Act and the Memorandum and Articles of Association, is in full force and effect and that the statutory pre-emption rights have been disapplied in respect of any allotment and issuance of the Shares;

3.8 that the Company will continue to renew its authority to allot and issue the Shares in accordance with the terms and conditions set out in the Memorandum and Articles of Association and Companies Act and that, where such authority has not been renewed, the Company will not allot or issue the Shares after such authority has expired;

3.9 that from the date of the board resolutions set out in Schedule, no other corporate or other action has been taken by the Company to amend, alter or repeal those resolutions;

Authenticity and bona fides

3.10 the completeness and authenticity of all documents submitted to us as originals or copies of originals and (in the case of copies) conformity to the originals of copy documents and the genuineness of all signatories, stamps and seals thereon;

3.11 where incomplete Plan Documents have been submitted to us or signature pages only have been supplied to us for the purposes of issuing this Opinion, that the originals of such Plan Documents correspond in all respects with the last draft of the complete Plan Documents submitted to us;

3.12 that the Plan Documents will be executed in a form and content having no material difference to the drafts provided to us, will be delivered by the parties thereto, and that the terms thereof will be observed and performed by the parties thereto;

3.13 that the copies produced to us of minutes of meetings and/or of resolutions correctly record the proceedings at such meetings and/or the subject matter which they purport to record and that any meetings referred to in such copies were duly convened, duly quorate and held, that those present at any such meetings were entitled to attend and vote at the meeting and acted bona fide throughout and that no further resolutions have been passed or other action taken which would or might alter the effectiveness thereof and that such resolutions have not been amended or rescinded and are in full force and effect;

3.14 that the Memorandum and Articles of Association of the Company amended on 25 May 2016 are the current Memorandum and Articles of Association of the Company, are up to date and have not been amended or superseded and that there are no other terms governing the Shares other than those set out in the Memorandum and Articles of Association of the Company;

3.15 that there is, at the relevant time of the allotment and issue of the Shares, no matter affecting the authority of the Directors to allot and issue the Shares, not disclosed by the Memorandum and Articles of Association or the resolutions produced to us, which would have any adverse implications in relation to the opinions expressed in this Opinion;

Accuracy of Searches and Warranties

3.16 the accuracy and completeness of the information disclosed in the Searches is accurate as of the date of this Opinion and that such information has not since the time of such search or enquiry been altered. It should be noted that:

(a) the matters disclosed in the Searches may not present a complete summary of the actual position on the matters we have caused searches to be conducted for;

(b) the position reflected by the Searches may not be fully up-to-date (and this risk may be higher while emergency measures introduced by the Irish Government in light of the COVID-19 pandemic remain in place); and

(c) searches at the Companies Registration Office, Dublin, do not necessarily reveal whether or not a prior charge has been created or a resolution has been passed or a petition presented or any other action taken for the winding-up of or the appointment of a receiver or an examiner to the Company or its assets.

3.17 that there has been no alterations in the status or condition of the Company as disclosed by the Searches.

3.18 the truth, completeness and accuracy of all representations and statements as to factual matters contained in the Plan Documents.

Solvency and Insolvency

3.19 that:

(a) the Company is at the date of this Opinion able to pay its debts within the meaning of Sections 509(3) and 570 of the Companies Act or any analogous provisions under any applicable laws; and

(b) the Company will not as a consequence of doing any act or thing which the Plan Documents contemplate, permit or require any relevant party to do, be unable to pay its debts within the meaning of such Sections or any analogous provisions under any applicable laws.

3.20 that:

(a) no liquidator, receiver or examiner or other similar or analogous officer has been appointed in relation to the Company any of the assets or undertakings; and

(b) no petition for the making of a winding-up order or the appointment of an examiner or any similar officer or any similar or analogous procedure in any jurisdiction has been presented in relation to the Company.

Commercial Benefit

3.21 that the Plan Documents have been entered into for bona fide commercial purposes, on arm’s length terms and for the benefit of each party thereto and are in those parties’ respective commercial interests and for their respective corporate benefit.

4. Disclosure

This Opinion is addressed to you in connection with the registration of the Shares with the SEC. We hereby consent to the inclusion of this Opinion as an exhibit to the Registration Statement to be filed with the SEC. In giving this consent, we do not thereby admit that we are in a category of persons whose consent is required under Section 7 of the Securities Act.

Yours faithfully

/s/ Arthur Cox

ARTHUR COX

SCHEDULE

The Plan Documents

1. A copy of the form of the Registration Statement to be filed by the Company with the SEC on or about the date of this Opinion;

2. A copy of the 2018 Plan;

3. A copy of the 2008 Plan;

4. A copy of the 2011 Plan;

5. A copy of the resolutions of shareholders of the Company regarding the approval of, among other things, the adoption of the 2008 Plan and the 2011 Plan, dated 16 September 2011;

6. A copy of the resolutions of the board of directors of the Company regarding the approval of, among other things, the adoption of the 2008 Plan and the 2011 Plan, dated 16 September 2011;

7. A copy of the resolutions of the board of directors of the Company delegating to the compensation committee of the board of directors of the Company the authority to approve, among other things, the 2018 Plan, dated 15-16 February 2018;

8. A copy of the resolutions of the compensation committee of the board of directors of the Company regarding the approval and adoption of, among other things, the 2018 Plan, dated 29 March 2018;

9. A copy of the resolutions of the board of directors of the Company approving, among other things, the preparation, execution and filing of a registration statement on Form S-8 (in respect of 4,400,000 Ordinary Shares of the Company under the 2018 Plan), dated 23-24 May 2018;

10. A copy of the resolutions of the board of directors of the Company delegating to the compensation committee of the board of directors of the Company the authority to approve a request for an additional increase in Ordinary Shares available under the 2018 Plan, dated 12 February 2020;

11. A copy of the resolutions of the compensation committee of the board of directors of the Company related to, among other things, an additional increase in Ordinary Shares available under the 2018 Plan, dated 27 March 2020;

12. A copy of the resolutions of the board of directors of the Company that, among other things, gave authority for the preparation, execution and filing of the Registration Statement in respect of the Shares at a meeting of the board of directors of the Company dated 20 May 2020;

13. A corporate certificate of the Secretary of the Company dated 29 July 2020 (the “Corporate Certificate”) certifying, among other things: (A) the voting results regarding approval of, among other things, (i) the amendment to the 2011 Plan increasing the number of Ordinary Shares for issuance under the 2011 Plan by 4,200,000 at the annual general meeting of the shareholders of the Company held on 1 August 2012; (ii) the amendment to the 2011 Plan increasing the number of Ordinary Shares for issuance under the 2011 Plan by 3,600,000 at the annual general meeting of the shareholders of the Company held on 1 August 2013; (iii) the amendment to the 2011 Plan increasing the number of Ordinary Shares for issuance under the 2011 Plan by 3,600,000 at the annual general meeting of the shareholders of the Company held on 28 May 2014; (iv) the amendment to the 2011 Plan increasing the number of Ordinary Shares for issuance under the 2011 Plan by 8,899,500 at the annual general meeting of the shareholders of the Company held on 25 May 2016;  (v): the 2018 Plan by the shareholders of the Company

at the annual general meeting of the shareholders of the Company held on 23 May 2018, (vi) the 2018 Plan, as amended to increase the number of Ordinary Shares for issuance thereunder by such number as approved at the annual general meeting of shareholders of the Company held on 20 May 2020; and (B) the voting results regarding, among other things, the approval of the granting of authority to the board of directors to allot shares up to an aggregate nominal amount equal to the authorised but unissued share capital of the Company, and to opt out of statutory pre-emption rights in respect of those equity securities, at the annual general meeting of the shareholders of the Company held on 24 May 2017;

14. A copy of the memorandum and articles of association of the Company in the form adopted by resolution of the shareholders of the Company on 25 May 2016;

15. A copy of the certificate of incorporation of the Company dated 4 May 2011;

16. A copy of the certificate of incorporation on re-registration as a public limited company dated 25 July 2011;

17. A copy of the certificate of incorporation on change of name of the Company dated 14 September 2011; and

18. Letter of Status from the Irish Companies Registration Office dated 27 July 2020.