Exhibit 24.2

POWER OF ATTORNEY
FOR EXECUTING FORM 3, FORM 4,
FORM 5 AND FORM 144

The undersigned hereby constitutes and appoints each of David Kronenfeld, Derek Ching and Ana Fernandez Cortez, with full power of substitution, as the undersigned’s true and lawful attorney-in-fact to:

(1)

Execute for and on behalf of the undersigned any Form 3, Form 4, and Form 5 in accordance with Section 16(a) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and any Form 144 in accordance with Rule 144 under the Securities Act of 1933 (the “Securities Act”), in each case including any amendments thereto, but only to the extent such form relates to the undersigned’s beneficial ownership of securities of USA Rare Earth, Inc. or any of its subsidiaries (collectively, the “Company”);

(2)

Do and perform any and all acts for and on behalf of the undersigned that may be necessary or desirable to complete and execute any Form ID, Form 3, Form 4, Form 5, or Form 144 (including amendments thereto) and timely file the form with the Securities and Exchange Commission and any stock exchange or quotation system, self-regulatory association or any other authority, and provide a copy as required by law or advisable to such persons as the attorney-in-fact deems appropriate; and

(3)

Take any other action in connection with the foregoing that, in the opinion of the attorney-in-fact, may be of benefit to, in the best interest of or legally required of the undersigned, it being understood that the documents executed by the attorney-in-fact on behalf of the undersigned pursuant to this Power of Attorney shall be in the form and shall contain the terms and conditions as the attorney-in-fact may approve in the attorney-in-fact’s discretion.

The undersigned hereby grants to the attorney-in-fact full power and authority to do and perform all and every act requisite, necessary or proper to be done in the exercise of any of the rights and powers herein granted, as fully to all intents and purposes as the undersigned might or could do if personally present, with full power of substitution or revocation, hereby ratifying and confirming all that the attorney-in-fact shall lawfully do or cause to be done by virtue of this Power of Attorney and the rights and powers granted herein. The undersigned acknowledges that the attorney-in-fact, in serving in such capacity at the request of the undersigned, is not assuming (nor is the Company assuming) any of the undersigned’s responsibilities to comply with Section 16 of the Exchange Act.

The undersigned agrees that the attorney-in-fact may rely entirely on information furnished orally or in writing by or at the direction of the undersigned to the attorney-in-fact. The undersigned also agrees to indemnify and hold harmless the Company and the attorney-in-fact against any losses, claims, damages or liabilities (or actions in these respects) that arise out of or are based upon any untrue statements or omissions of necessary facts in the information provided by or at the direction of the undersigned, or upon the lack of timeliness in the delivery of information by or at the direction of the undersigned, to the attorney-in fact for purposes of executing, acknowledging, delivering or filing a Form ID, Form 3, Form 4, Form 5 or Form 144 (including amendments thereto), and agrees to reimburse the Company and the attorney-in-fact on demand for any legal or other expenses reasonably incurred in connection with investigating or defending against any such loss, claim, damage, liability or action.

This Power of Attorney shall remain in full force and effect until the undersigned is no longer required to file any Form 3, Form 4, Form 5 or Form 144 with respect to the undersigned’s holdings of and transactions in securities issued by the Company, unless earlier revoked by the undersigned in a signed writing delivered to the attorney-in-fact. This Power of Attorney does not revoke any other power of attorney that the undersigned has previously granted.

IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be executed as of the date written below.

Bayshore Rare Earths II, LLC

/s/ Tready Smith
signature

Tready Smith, CEO
Type or Print Name

September 18, 2025
Date

Bayshore Capital Advisors, LLC 4