Exhibit 4.1

EOS ENERGY ENTERPRISES, INC.

[Holder Information]

EOS ENERGY ENTERPRISES, INC. RIGHTS CERTIFICATE

RIGHTS CERTIFICATE TO SUBSCRIBE FOR UNITS FOR HOLDERS OF RECORD OF EOS ENERGY ENTERPRISES, INC. COMMON STOCK OR WARRANTS ISSUED ON APRIL 14, 2023, MAY 17, 2023, DECEMBER 19, 2023 AND NOVEMBER 21, 2025 AT 5:00 P.M., NEW YORK CITY TIME, ON JULY 1, 2026. EXERCISABLE ON OR BEFORE 5:00 P.M., NEW YORK CITY TIME, ON JULY 21, 2026, UNLESS EXTENDED BY THE COMPANY.

As the registered owner of the rights certificate below (the “Rights Certificate”), you are entitled to subscribe for the number of units (the “Units”, and each, a “Unit”) of Eos Energy Enterprises, Inc., a Delaware corporation (the “Company”), shown above and below. Each whole transferable subscription right (each a “Right”) entitles the holder (the “Rights Holder”) to subscribe for and purchase 0.071193 of a Unit of the Company (the “Basic Subscription Rights”), with each unit consisting of one share of common stock, par value $0.0001 per share (the “Common Stock”) and 0.4388 of a warrant to purchase one share of Common Stock at an exercise price of $5.481 per whole share (the “Warrants”), at a subscription price per full Unit equal to $5.481 (the “Subscription Price”), pursuant to a rights offering (the “Rights Offering”). If any Units available for purchase in the Rights Offering are not purchased by the Rights Holders pursuant to the exercise of their Basic Subscription Rights (the “Excess Units”), any Rights Holder fully exercising its Basic Subscription Rights hereunder may also subscribe for a number of Excess Units pursuant to the terms and conditions of the Rights Offering, subject to proration (the “Over-subscription Privilege”) as described in the prospectus supplement relating to the Rights Offering, dated July 2, 2026, including the accompanying prospectus (the “Prospectus Supplement”).

If you choose to exercise your Rights, your completed Rights Certificate must be received by 5:00 p.m., New York City time, on July 21, 2026, which is the Expiration Time (unless extended by the Company). If you choose to sell or transfer your Rights, your completed Rights Certificate must be received by the Subscription Agent by 11:00 A.M., New York City time, on July 14, 2026 (five business days prior to the Expiration Time, as may be adjusted in the event of an extension of the Expiration Time). If you intend on making your cash payment of the Subscription Price by uncertified check, you should ensure that the Subscription Agent receives the appropriate materials by July 14, 2026 (at least five business days prior to the Expiration Time). If you are a registered foreign holder and choose to exercise your Rights, you must notify the Subscription Agent on or before 11:00 a.m., New York City time, on July 14, 2026 (the fifth business day prior to the Expiration Time), and must establish to the satisfaction of the Subscription Agent that such exercise is permitted under applicable law.

FOR A MORE COMPLETE DESCRIPTION OF THE TERMS AND CONDITIONS OF THE RIGHTS OFFERING, PLEASE REFER TO THE PROSPECTUS SUPPLEMENT, WHICH IS INCORPORATED HEREIN BY REFERENCE. COPIES OF THE PROSPECTUS SUPPLEMENT ARE AVAILABLE UPON REQUEST FROM THE INFORMATION AGENT, SODALI & CO., at (203) 658-9400 (FOR BANKS AND BROKERS) OR (833) 225-0490 (TOLL FREE) OR BY E-MAIL AT EOSE.info@investor.sodali.com.

EXERCISABLE ON OR BEFORE 5:00 P.M., NEW YORK CITY TIME, ON July 21, 2026
UNLESS EXTENDED BY THE COMPANY (THE “EXPIRATION TIME”)

(Complete appropriate section on subsequent pages of this form.)

The Company is conducting a Rights Offering, which entitles holders of the Company’s Common Stock and warrants issued on April 14, 2023, May 17, 2023, December 19, 2023 and November 21, 2025 (the “Participating Warrants”) to receive a Right for each share of Common Stock or Participating Warrant held by them as of 5:00 P.M. New York City time, on July 1, 2026 (the “Record Date”). Each whole Right entitles the holder to subscribe for and purchase 0.071193 of a Unit pursuant to its Basic Subscription Rights and, if its Basic Subscription Rights are fully exercised, to subscribe for additional Units pursuant to its Over-subscription Privilege. If the aggregate Subscription Price delivered or transmitted by the Rights Holder with the Rights Certificate exceeds the aggregate Subscription Price for all Units for which the Rights Holder would be entitled to subscribe pursuant to its Basic Subscription Rights and no direction is given as to the excess, such Rights Holder will be deemed to have subscribed for a number of Excess Units equal to the maximum whole number of Excess Units that could be purchased with such excess Subscription Price. Each Unit consists of one share of Common Stock and 0.4388 of a Warrant. Shares of Common Stock and Warrants purchased pursuant to the Rights Offering will be issued by the Transfer Agent as soon as practicable following the Expiration Time. No fractional Rights or cash in lieu thereof were issued or paid and fractional Rights were rounded down to the nearest whole Right, as described in the Prospectus Supplement. Fractional Units resulting from the exercise of the Rights will be eliminated by rounding down to the nearest whole number, with the total subscription payment being adjusted accordingly. Set forth herein is the number of Rights evidenced by this Rights Certificate that the Rights Holder is entitled to exercise pursuant to such Rights Holder’s Basic Subscription Rights. If shares of Common Stock or Participating Warrants applicable to a subscription are held by more than one record holder, the Rights Certificate must be signed by each such holder; if a holder or joint holders (registrants) hold more than one position in the Company, as indicated by different accounts on the relevant record holder list, then separate, properly completed and executed Rights Certificates must be submitted for each such position held by that or those joint holders (registrants).

The Company retains the right to terminate the Rights Offering at any time and for any reason prior to the Expiration Time.

This Rights Certificate is transferable, and may be combined or divided (but only into Rights Certificates evidencing full rights) at the office of the Subscription Agent. Rights Holders should be aware that if they choose to exercise, assign, transfer or sell only part of their Rights they may not receive a new Rights Certificate in sufficient time to exercise, assign, transfer or sell the remaining Rights evidenced thereby.

Signature(s) Guaranteed by:

IMPORTANT: The signature(s) should be guaranteed by an eligible guarantor institution (bank, stock broker, savings & loan association or credit union) with membership in an approved signature guarantee medallion program pursuant to Securities and Exchange Commission Rule 17Ad-15.

For questions and to request copies of materials, call the Information Agent – Sodali & Co.,
at (203) 658-9400 (for banks and brokers) or (833) 225-0490  (toll free) or by e-mail at EOSE.info@investor.sodali.com

Please complete and return, as described below, on or before the dates outlined below.

SUBSCRIPTION AGENT: Broadridge Corporate Issuer Solutions, LLC

To participate in the Rights Offering available through your shares held through Broadridge you must follow the instructions and complete the relevant section(s) below, sign and date the front page of this document, and return this signed Rights Certificate, with payment or any additional documents if applicable, to the Subscription Agent listed above. Check all boxes below that apply.

To subscribe for shares under the Basic Subscription Rights, please complete Sections 1.A and 1.C below. If you wish to subscribe for shares under the Over-subscription Privilege as well, you must also complete Section 1.B below. This Form of Exercise, Sale or Transfer and payment to the Subscription Agent must be received by 5:00 p.m., New York City time, on July 21, 2026, which is the Expiration Time (unless extended by the Company). Funds must clear your account before the Expiration Time. If you intend on making your cash payment of the Subscription Price by uncertified check, you should ensure that the Subscription Agent receives the appropriate materials at least five business days prior to the Expiration Time. Please see paragraph 1 of the instructions accompanying this Rights Certificate.

☐ A. Basic Subscription Rights: By checking this box, you will exercise your Rights at the discounted price of $5.481 per Unit. Please complete the fields below.

Example:

100 Units x $5.481 = $548.10

☐ B. Over-subscription Privilege: By checking this box, you will exercise your right to oversubscribe for additional shares (only available when you fully subscribe for the Rights available to you in Section 1.A above). Please complete the fields below.

Please indicate any changes of address for deliveries and payments, if applicable:

I hereby irrevocably subscribe for the number of Units indicted as the total of Sections 1.A and 1.B above upon the terms and conditions specified in the Prospectus Supplement relating thereto and incorporated by reference herein, receipt of which is acknowledged. I hereby agree that if I fail to pay for the Units for which I have subscribed, the Company may exercise any remedies available to it under law.

If the aggregate Subscription Price paid by a Rights Holder is insufficient to purchase the number of Units that the holder indicates are being subscribed for, or if a Rights Holder does not specify the number of Units to be purchased, or if the aggregate Subscription Price paid by a Rights Holder exceeds the amount necessary to purchase the number of Units for which the Rights Holder has indicated an intention to subscribe, then the Rights Holder will be deemed to have exercised first its Basic Subscription Rights and second its Over-subscription Privilege to purchase a number of Units equal to the maximum whole number of shares that could be purchased with the payment tendered.

MAKE CHECKS PAYABLE TO: Broadridge Corporate Issuer Solutions, LLC

DELIVERY OF THIS FORM OF EXERCISE, SALE OR TRANSFER TO AN ADDRESS OTHER THAN AS SET FORTH ABOVE DOES NOT CONSTITUTE A VALID DELIVERY.

Full payment for shares subscribed for both the Basic Subscription Rights (Section 1.A) and the Over-subscription Privilege (Section 1.B) must accompany this Rights Certificate or a notice of guaranteed delivery. Please reference your Rights Certificate Number (found on the front of this Rights Certificate) on your check, bank draft, money order or notice of guaranteed delivery. Funds must clear your account before the Expiration Time. If you intend on making your cash payment of the Subscription Price by uncertified check, you should ensure that the Subscription Agent receives the appropriate materials at least five business days prior to the Expiration Time. You may, at your option, wire your immediately available funds to the Subscription Agent. Before sending your wire, please contact the Subscription Agent at 1-888-789-8409 to advise them of your intent to wire funds and to obtain wire instructions. This will ensure prompt and accurate credit upon receipt of your wire. Please contact the information agent for further information.

FOR RIGHTS HOLDERS REMITTING PAYMENT BY UNCERTIFIED PERSONAL CHECK, ANY FAILURE WHATSOEVER, REGARDLESS OF THE CAUSE OR NATURE OF SUCH FAILURE, OF THE SUBSCRIPTION AGENT TO RECEIVE YOUR PAYMENT OF THE SUBSCRIPTION PRICE FREE AND CLEAR BY THE EXPIRATION TIME SHALL RESULT IN THE CANCELLATION OF YOUR EXERCISES OF RIGHTS, AND YOUR RIGHTS WILL EXPIRE NULL AND VOID WITHOUT PAYMENT OF ANY COMPENSATION THEREFOR.

2.    ☐ Sell Your Rights: By checking the box for this section, you authorize the Subscription Agent to attempt to sell your unexercised Rights according to the procedures described in the Prospectus Supplement. If you choose to sell your Rights, your completed Rights Certificate (together with a properly completed and executed Internal Revenue Service Form W-8 or W-9, as applicable) must be received by the Subscription Agent by 11:00 A.M., New York City time, on July 14, 2026 (five business days prior to the Expiration Time, as may be adjusted in the event of an extension of the Expiration Time). Please see Paragraph 2 of the Instructions accompanying the Rights Certificate for timing considerations relating to the sale of rights.

Please indicate any changes of address for deliveries and payments, if applicable:

3.    ☐ Transfer Your Rights: If you want some or all of your unexercised Rights transferred to a designated transferee, or to a bank or broker to sell for you, check the box for this section and complete the requested information below. If you choose to transfer your Rights, your completed Rights Certificate (together with a properly completed and executed Internal Revenue Service Form W-8 or W-9, as applicable) must be received by the Subscription Agent by 11:00 A.M., New York City time, on July 14, 2026 (five business days prior to the Expiration Time, as may be adjusted in the event of an extension of the Expiration Time).  Please see Paragraph 3 of the Instructions accompanying this Rights Certificate for timing considerations relating to the transfer of Rights.

For value received,                              of the Rights represented by this Form of Exercise, Sale or Transfer are assigned to:

Print Full Name of Bank or Broker or Assignee and Assignee’s Social Security Number

__________________________________

Print Full Address of Bank or Broker or Assignee    ________________________________________________________

Signature(s) of Assignor(s)   _________________________________________________________________________

4.    ☐ New Certificate for Unexercised Rights:  If you want a new Rights Certificate evidencing any unexercised Rights delivered to you or to someone else, please complete the requested information below. Please see the Instructions accompanying this Rights Certificate for timing considerations relating to requesting a new Rights Certificate.

Print Rights Holder’s Full Name and Social Security Number Address for delivery of certificate representing unexercised Rights (if any)

5. Signature:

The signature(s) on this Form of Exercise, Sale or Transfer must correspond with the name(s) of the registered holder(s) exactly as it appears on the face of the Rights Certificate without any alteration or change whatsoever. In the case of joint registered holders, each person must sign this Form of Exercise, Sale or Transfer in accordance with the foregoing. If you sign this Form of Exercise, Sale or Transfer in your capacity as a trustee, executor, administrator, guardian, attorney-in- fact, agent, officer or a corporation or other fiduciary or representative, you must indicate the capacity in which you are signing when you sign and, if requested by the Subscription Agent in its sole and absolute discretion, you must present to the Subscription Agent satisfactory evidence of your authority to sign in that capacity.

If you wish to transfer your Rights, then your signature must be guaranteed by an Eligible Guarantor Institution, as that term is defined in Rule 17Ad-15 of the Securities Exchange Act of 1934, as amended, with membership in an approved signature guarantee medallion program pursuant to that rule, which may include: (a) a commercial bank or trust company; (b) a member firm of a domestic stock exchange; or (c) a savings bank or credit union.

DELIVERY OF THIS FORM OF EXERCISE, SALE OR TRANSFER TO AN ADDRESS OTHER THAN AS SET FORTH ABOVE DOES NOT CONSTITUTE A VALID DELIVERY.