MPT OF NACOGDOCHES FCER, LLC, MPT OF MESA, LLC MPT OF PORTARTHUR, LLC, MPT OF WEST MONROE, LLC, MPT OF DALLAS, LLC MPT RHM HOLDCO, MPT RHM SONNENWENDE, MPT RHMKLAUS, MPT RHM VESALIUS, MPTRHM PARK, MPT RHM FONTANA, MPT RHM HILLERSBACH and MPT RHM CHRISTIAAN, as Guarantors, MPT OPERATING PARTNERSHIP, L.P. and MPT FINANCE CORPORATION, as Issuers, MEDICAL PROPERTIESTRUST, INC., as Parent and a Guarantor, the other GUARANTORS named herein, as Guarantors, and WILMINGTON TRUST, NATIONAL ASSOCIATION, as Trustee THIRDSUPPLEMENTAL INDENTURE Dated as of December 20, 2013 To INDENTURE Dated as of October 10, 2013 5.70% Senior Notes due 2020 THIRD SUPPLEMENTAL INDENTURE

Exhibit 4.31

MPT OF NACOGDOCHES FCER, LLC,

MPT OF MESA, LLC

MPT OF PORT ARTHUR, LLC,

MPT OF WEST MONROE, LLC,

MPT OF DALLAS, LLC

MPT RHM HOLDCO,

MPT RHM SONNENWENDE,

MPT RHM KLAUS,

MPT RHM VESALIUS,

MPT RHM PARK,

MPT RHM FONTANA,

MPT RHM HILLERSBACH

and

MPT RHM CHRISTIAAN,

as Guarantors,

MPT OPERATING PARTNERSHIP, L.P.

and

MPT FINANCE CORPORATION,

as Issuers,

MEDICAL PROPERTIES TRUST, INC.,

as Parent and a Guarantor,

the other GUARANTORS named herein,

as Guarantors,

and

WILMINGTON TRUST, NATIONAL ASSOCIATION,

as Trustee

THIRD SUPPLEMENTAL INDENTURE

Dated as of December 20, 2013

To

INDENTURE

Dated as of October 10, 2013

5.70% Senior Notes due 2020

THIRD SUPPLEMENTAL INDENTURE

THIRD SUPPLEMENTAL INDENTURE (this “Third Supplemental Indenture”), dated as of December 20, 2013, by and among MPT of Nacogdoches FCER, LLC, a Delaware limited liability company, MPT of Mesa, LLC, a Delaware limited liability company, MPT of Port Arthur, LLC, a Delaware limited liability company, MPT of West Monroe, LLC, a Delaware limited liability company, MPT of Dallas, LLC, a Delaware limited liability company (the “Domestic Guarantors”), and MPT RHM Holdco, MPT RHM Sonnenwende, MPT RHM Klaus, MPT RHM Vesalius, MPT RHM Park, MPT RHM Fontana, MPT RHM Hillersbach, MPT RHM Christiaan, each a société à responsabilité limitée incorporated and existing under the laws of the Grand Duchy of Luxembourg (the “Lux Guarantors” and together with the Domestic Guarantors, the “New Guaranteeing Subsidiaries”), MPT Operating Partnership, L.P., a Delaware limited partnership (“Opco”), MPT Finance Corporation, a Delaware corporation (“Finco” and, together with Opco, the “Issuers”), Medical Properties Trust, Inc., a Maryland corporation (the “Parent”), as Guarantor, each of the other Guarantors (as defined in the Indenture), as Guarantors, and Wilmington Trust, National Association, existing under the laws of the United States of America, as Trustee (the “Trustee”).

WITNESSETH

WHEREAS, the Issuers and the Guarantors have heretofore executed and delivered an Indenture, dated as of October 10, 2013 (the “Base Indenture”), as supplemented by that certain First Supplemental Indenture, dated as of October 10, 2013 (the “First Supplemental Indenture”) and by that certain Second Supplemental Indenture, dated October 30, 2013 (the “Second Supplemental Indenture”, and together with the First Supplemental Indenture and the Base Indenture, the “Indenture”), providing for the issuance by the Issuers of the 5.750% Senior Notes due 2020 (the “Notes”);

WHEREAS, pursuant to Section 10.01(a)(4) of the Indenture, the Parent, the Issuers, the Guarantors and the Trustee, together, may supplement the Indenture without notice to or the consent of any Holders or any other party to the Indenture in order to add Guarantees with respect to the Notes;

WHEREAS, as of November 21, 2013, the Domestic Guarantors guaranteed the Credit Agreement, with the exception of MPT of Dallas, LLC, and pursuant to Section 5.14(a) of the Indenture, the Domestic Guarantors are required to become Guarantors under the Indenture;

WHEREAS, the Indenture requires that an entity that constitutes a Guarantor shall join the Issuers and the existing Guarantors in executing and delivering to the Trustee a supplemental indenture pursuant to which such entity shall unconditionally Guarantee, on a joint and several basis, the full and prompt payment of the principal of, premium, if any, and interest in respect of the Notes on a senior basis and all other obligations under the Indenture;

WHEREAS, the Lux Guarantors and MPT of Dallas, LLC wish to join the Issuers and the existing Guarantors in executing and delivering to the Trustee a supplemental indenture pursuant to which the Lux Guarantors and MPT of Dallas, LLC shall unconditionally Guarantee,

on a joint and several basis, the full and prompt payment of the principal of, premium, if any, and interest in respect of the Notes on a senior basis and all other obligations under the Indenture; and

WHEREAS, pursuant to Section 10.06 of the Indenture, the Trustee is authorized to execute and deliver this Third Supplemental Indenture.

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, the Issuers, the Guarantors, the Trustee and the New Guaranteeing Subsidiaries mutually covenant and agree for the equal and ratable benefit of the Holders of the Notes as follows:

1. CAPITALIZED TERMS. Capitalized terms used herein without definition shall have the meanings assigned to them in the Indenture. The rules of interpretation set forth in the Indenture shall be applied here as if set forth in full herein.

2. AGREEMENT TO GUARANTEE. The New Guaranteeing Subsidiaries hereby agree to provide unconditional Guarantees on the terms and subject to the conditions set forth in the Indenture including, but not limited to, Article 11 thereof.

3. MISCELLANEOUS PROVISIONS.

(a) The Trustee makes no undertaking or representation in respect of, and shall not be responsible in any manner whatsoever for and in respect of, the validity or sufficiency of this Third Supplemental Indenture or the proper authorization or the due execution hereof by the Issuers or for or in respect of the recitals and statements contained herein, all of which recitals and statements are made solely by the Issuers.

(b) On the date hereof, the Indenture shall be supplemented and amended in accordance herewith, and this Third Supplemental Indenture shall form part of the Indenture for all purposes, and the Holder of every Note heretofore or hereafter authenticated and delivered under the Indenture shall be bound thereby. The Trustee accepts the trusts created by the Indenture, as amended and supplemented by this Third Supplemental Indenture, and agrees to perform the same upon the terms and conditions of the Indenture, as amended and supplemented by this Third Supplemental Indenture.

(c) This Third Supplemental Indenture shall be deemed to be incorporated in, and made a part of, the Indenture. The Indenture, as amended and supplemented by this Third Supplemental Indenture, shall be read, taken and construed as one and the same instrument and all the provisions of the Indenture shall remain in full force and effect in accordance with the terms thereof and as amended and supplemented by this Third Supplemental Indenture.

(d) THIS THIRD SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

(e) This Third Supplemental Indenture may be executed in any number of counterparts, each of which so executed shall be deemed to be an original, but all such counterparts shall together constitute but one and the same instrument.

IN WITNESS WHEREOF, the parties hereto have caused this Third Supplemental Indenture to be duly executed and attested, all as of the date first above written.

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