EXHIBIT 4.31

                   AMENDMENT TO SECURED CONVERTIBLE NOTE


          THIS AMENDMENT TO SECURED CONVERTIBLE NOTE (this "Amendment") is made
and entered into as of the 28th day of October, 2003, by and among Tsunami
Partners, L.P. (the "Payee"), having an address at 2011 Cedar Springs Road, Apt.
506, Dallas, Texas 75201, and U.S. Energy Corp. (the "Maker"), having its
principal place of business at 877 North 8th West, Riverton, Wyoming 82501.
Capitalized terms used and not defined herein have the meanings set forth in the
Note (as defined below).

                                   BACKGROUND

          A. The Maker entered into an 8% Secured Convertible Note in favor of
the Payee on November 19, 2002 in the principal amount of $500,000 (the "Note").

          B. The Maker and the Payee each desire to provide for an extension of
the Maturity Date of the Note, the accrual of interest after September 1, 2003,
and the mandatory conversion of all amounts due under the note as of the
Maturity Date into shares of the Maker's common stock.

          C. In order to effect the foregoing, the parties have agreed to amend
the Note, as more particularly set forth herein.

          NOW, THEREFORE, in consideration of the promises and the mutual
representations, warranties, covenants and agreements hereinafter set forth, and
upon the terms and subject to the conditions hereinafter set forth, the Maker
and Payee, each intending to be legally bound, hereby agree as follows:

                                    ARTICLE 1
                                Amendment of Note

          1.1. Amendment to Section 1. Section 1 of the Note is hereby amended
and restated as follows:

     "1. Maturity. Except to the extent earlier converted in accordance
     with Section 6, the entire amount outstanding under this Note
     (principal and interest) will be due and payable at the aforesaid
     address of Payee or such other place as Payee may designate on
     December 31, 2004 (the "Maturity Date")."

          1.2 Amendment to Section 2. Section 2 of the Note is hereby amended
and restated as follows:

     "2. Payment of Interest. Interest on the principal outstanding under
     this Note shall be payable on the first business day of each June,
     September, December and March (each an "Interest Payment Date")
     commencing September 1, 2002 until the entire principal balance and
     accrued interest is paid in full or converted in accordance with
     Section 6. All interest accruing on the outstanding principal
     hereunder from and after the September 1, 2003 Interest Payment Date
     shall not be payable quarterly in cash but shall instead be added to
     the principal outstanding under this Note."







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          1.3 Amendment to Section 3. Section 3 of the Note is hereby amended
and restated as follows:

     "3. Pre-Default Interest Rate. Prior to the occurrence of an Event of
     Default (as hereinafter defined), the outstanding principal balance of
     this note shall bear interest at a rate per annum (the "Pre-Default
     Rate") equal to the Federal Short Term Rate for annual compounding
     (the "Federal Short Term Rate") (as such term is defined in Section
     l274(d) of the Internal Revenue Code), with changes in the interest
     rate hereunder occurring coincident with changes in such Federal Short
     Term Rate."

          1.4 Amendment to Section 5. All of Section 5 of the Note is hereby
deleted.

          1.5 Amendment to Section 6. Section 6 of the Note is hereby amended
and restated as follows:

     "6. Conversion.

               a. Optional Conversion. At any time and from time to time
     prior to repayment of all amounts due under the Note, the principal
     amount of the Note and accrued and unpaid interest thereon shall be
     convertible at the option of the Payee into fully paid and
     non-assessable shares of common stock of either (x) the Maker ("USEG
     Common Stock") or (y) Rocky Mountain Gas, Inc. ("RMG Common Stock",
     and, together with USEG Common Stock, "Common Stock"); provided,
     however, that each conversion effected pursuant to this sentence shall
     be in an amount which is no less than the lesser of (i) $100,000 or
     (ii) the amount outstanding under the Note at the time of such
     conversion. The number of shares of USEG Common Stock or RMG Common
     Stock, as the case may be, that Payee shall be entitled to receive
     upon conversion shall be equal to the number attained by dividing the
     amount of the Note being converted by the Conversion Price. The term
     "Conversion Price" shall mean $2.25 with respect to any amount of this
     Note converted into USEG Common Stock and $1.50 with respect to any
     amount of this Note converted into RMG Common Stock.

                    1. In order to exercise the conversion privilege pursuant to
     this Section 6(a), Payee shall surrender this Note, duly endorsed, to
     Maker's address set forth above, and shall give written notice of
     conversion to Maker stating Payee's election to convert this Note or
     the portion thereof specified in said notice. As promptly as
     practicable after the surrender of this Note as aforesaid, Maker or
     Rocky Mountain Gas, Inc. ("RMG" and, together with the Maker, the
     "Companies" and each individually a "Company"), as applicable, shall
     issue and shall deliver to Payee a certificate or certificates for the
     number of full shares of Common Stock issuable upon the conversion of
     this Note or portion thereof registered in the name of Payee in
     accordance with the provisions of this Section 6(a) and a check or
     cash in respect of any fractional interest in respect of a share of
     Common Stock arising upon such conversion, as provided below. In case
     this Note shall be surrendered for partial conversion, the Maker shall
     execute and deliver to Payee, without charge, a new Note in an
     aggregate principal amount equal to the unconverted portion of the
     surrendered Note. If the Payee elects to exercise the conversion
     privilege set forth in this Section 6(a) only as to interest, the
     Payee shall not be required to surrender this Note.


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                    2. Each conversion effected pursuant to this Section 6(a)
     shall be deemed to have been effected on the date on which this Note
     shall have been surrendered and the conversion notice shall have been
     received by Maker, as aforesaid, and Payee shall be deemed to have
     become on said date the holder of record of the shares of Common Stock
     issuable upon such conversion.

                    3. No fractional shares of Common Stock or scrip
     representing fractional shares shall be issued upon conversion of this
     Note. If any fractional share of Common Stock would be issuable upon
     the conversion of this Note, Maker shall make an adjustment therefor
     in cash at the Conversion Price.

               b. Mandatory Conversion. Provided that no Event of Default
     has occurred and is continuing under the Note, the total amount
     outstanding under the Note as of the Maturity Date (including
     principal, accrued and unpaid interest and any fees due hereunder)
     shall, without further action on the part of any person, be
     automatically converted into shares of USEG Common Stock on the
     Maturity Date (the "Mandatory Conversion"). The number of shares of
     USEG Common Stock that Payee shall be entitled to receive upon the
     Mandatory Conversion shall be equal to the total amount outstanding
     under the Note divided by the Conversion Price for the USEG Common
     Stock."

          1.6 Amendment to Section 7. Section 7 of the Note is hereby amended
and restated as follows:

          7. Adjustments. The Conversion Price and the number of shares of
     Common Stock purchasable pursuant to this Note are subject to
     adjustment from time to time as follows:

               a. In the event a Company should at any time or from time to
     time after the date hereof fix a record date for the effectuation of a
     split or subdivision of the outstanding shares of Common Stock or the
     determination of holders of Common Stock entitled to receive a
     dividend or other distribution payable in additional shares of Common
     Stock or other securities or rights convertible into, or entitling the
     holder thereof to receive directly or indirectly, additional shares of
     Common Stock (hereinafter referred to as "Common Stock Equivalents")
     without payment of any consideration by such holder for the additional
     shares of Common Stock or the Common Stock Equivalents (including the
     additional shares of Common Stock issuable upon conversion or exercise
     thereof), then, as of such record date (or the date of such dividend
     distribution, split or subdivision if no record date is fixed), the
     Conversion Price shall be appropriately decreased so that the number
     of shares of Common Stock issuable on conversion of each share of such
     Common Stock shall be increased in proportion to such increase of
     outstanding shares.

               b. If the number of shares of Common Stock outstanding at
     any time after the date hereof is decreased by a combination of the
     outstanding shares of Common Stock, then following the record date of
     such combination, the Conversion Price shall be appropriately
     increased so that the number of shares of Common Stock issuable on
     conversion of this Note shall be decreased in proportion to such
     decrease in outstanding shares.


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               c. For further clarification and to eliminate any ambiguity,
     the term "Common Stock" as used in this Section 8 shall refer to USEG
     Common Stock if the "Company" for purposes of this Section 7 is the
     Maker or RMG Common Stock if the "Company" for purposes of this
     Section 7 is RMG."

          1.7 Amendment to Section 8. Section 8 of the Note is hereby amended
and restated as follows:

          8. Mergers, Consolidations, Sales. In the case of any
     consolidation or merger of a Company with another entity, or the sale
     of all or substantially all of its assets to another entity, or any
     reorganization or reclassification of the Common Stock or other equity
     securities of such Company, then, as a condition of such
     consolidation, merger, sale, reorganization or reclassification,
     lawful and adequate provision shall be made whereby Payee shall
     thereafter have the right to receive upon the basis and upon the terms
     and conditions specified herein and in lieu of the shares of Common
     Stock immediately theretofore issuable upon conversion of this Note,
     such shares of stock, securities or assets as may (by virtue of such
     consolidation, merger, sale, reorganization or reclassification) be
     issued or payable with respect to or in exchange for a number of
     outstanding shares of Common Stock equal to the number of shares of
     Common Stock immediately theretofore issuable upon conversion of this
     Note had such consolidation, merger, sale, reorganization or
     reclassification not taken place, and in any such case appropriate
     provisions shall be made with respect to the rights and interests of
     Payee to the end that the provisions hereof shall thereafter be
     applicable, as nearly as may be, in relation to any shares of stock,
     securities or assets thereafter deliverable upon conversion of this
     Note. Neither Company shall not effect any such consolidation, merger
     or sale, unless prior to or simultaneously with the consummation
     thereof, the successor entity (if other than such Company) resulting
     from such consolidation or merger or the entity purchasing such assets
     shall assume by written instrument executed and mailed or delivered to
     Payee, the obligation to deliver to Payee such shares of stock,
     securities or assets as, in accordance with this Section 8, Payee may
     be entitled to receive. For further clarification and to eliminate any
     ambiguity, the term "Common Stock" as used in this Section 8 shall
     refer to USEG Common Stock if the "Company" for purposes of this
     Section 9 is the Maker or RMG Common Stock if the "Company" for
     purposes of this Section 8 is RMG."

          1.8 Amendment to Section 11. Section 11 shall be amended to add the
following subsection (c):

     "c. Registration. If the Maker proposes to file a registration
     statement on Form S-3 with the SEC (a "Registration Statement"),
     either for its own account or for the account of others, the Maker
     shall, prior to filing such Registration Statement, provide written
     notice to the Payee of the Maker's intention to file such Registration
     Statement (a "Registration Notice"). Payee shall be entitled to
     register all or any portion of the Interest Shares held by such Payee
     by providing written notice (an "Acceptance Notice") to the Maker of
     Payee's election to participate in such registration. Each Acceptance
     Notice shall (i) be delivered to the Maker within thirty (30) days
     after receipt of the Registration Notice and (ii) specify the number
     of Interest Shares (as defined below) intended to be sold or disposed
     of by Payee. The Maker shall use its best efforts to cause all
     Interest Shares to be included in the Registration Statement. To the
     extent not inconsistent with the


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     foregoing, all benefits of the registration covenant contained in
     Section 5 of the Subscription Agreement shall be retained by Payee in
     connection with a registration of Interest Shares effected pursuant to
     this paragraph (c), and for purposes of applying said Section 5 to the
     Interest Shares, all references in said Section 5 to "Shares" shall be
     deemed to refer to the Interest Shares. For purposes of this Note, the
     term "Interest Shares" shall mean those shares of USEG Common Stock
     received by the Payee in connection with any conversion of accrued
     interest in accordance with Section 6 hereof."

                                    ARTICLE 2
                                  Miscellaneous

          2.1. Governing Law. This Amendment shall be construed and enforced in
accordance with the laws of the State of Wyoming.

          2.2. Severability. Whenever possible, each provision of this Amendment
will be interpreted in such manner as to be effective and valid under applicable
law, but if any provision of this Amendment is held to be invalid, illegal or
unenforceable in any respect under any applicable law or rule in any
jurisdiction, such invalidity, illegality or unenforceability will not affect
any other provision or the effectiveness or validity of any provision in any
other jurisdiction, and this Amendment will be reformed, construed and enforced
in such jurisdiction as if such invalid, illegal or unenforceable provision had
never been contained herein.

          2.3. Interpretation. Unless the context of this Amendment otherwise
requires, (i) words of any gender include each gender and the neuter; (ii) words
using the singular or plural number also include the plural or singular number,
respectively; (iii) the terms "hereof," "herein," "hereby" and derivative or
similar words refer to this entire Amendment; (iv) the terms "Article" or
"Section" refer to the specified Article or Section of this Amendment; and (v)
the term "including" or similar words shall be construed as to refer to such
matter without limitation thereof. The headings contained in this Amendment are
for reference purposes only and shall not affect in any way the meaning or
interpretation of this Amendment.

          2.4. Amendments. The provisions of this Amendment, including the
provisions of this sentence, may not be amended, modified or supplemented, and
waivers or consents to departures from the provisions hereof may not be given
without the written consent of the parties hereto.

          2.5. Entire Agreement. This Amendment, together with the Note,
contains the entire agreement and understanding between the parties with respect
to the subject matter of the Note, the Subscription Agreement, and that certain
Security Agreement by and between Maker and Caydal dated May 30, 2002 (the
"Security Agreement").

          2.6. Full Force and Effect. Other than as set forth herein, the terms
of the Note shall remain in full force and effect.

          2.7 Further Assurances. Maker hereby agrees to take all steps
necessary or desirable and to proceed diligently and in good faith to cause RMG
to comply with all provisions of the Note or this Amendment that require RMG to
take action or refrain from taking action, as the case may be.

          2.8 Ratification of Agreements.


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               2.8.1 Until the Note is fully paid or converted into Common
Stock, Caydal shall be, for purposes of Section 4 of the Subscription Agreement,
considered to hold Maker's indebtedness for borrowed money in an amount equal to
the amount then outstanding under the Note.

               2.82. Maker and Caydal each agree and acknowledge that the
Security Agreement shall remain in full force and effect until the amount
outstanding under the Note is paid in full or converted into Common Stock.

          2.9. No Waiver. Except as specifically set forth herein, the
execution, delivery and performance of this Amendment shall not operate as a
waiver of any right, power or remedy of the parties hereto under the Note and
the related agreements executed in connection therewith or constitute a waiver
of any provision thereof.

          2.10. Counterparts. This Amendment may be executed, including by
facsimile signature, in one or more counterparts, each of which when so executed
shall be deemed to be an original and all of which together shall constitute one
and the same instrument.



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          IN WITNESS WHEREOF, the parties hereto have executed this Amendment as
of the date first written above.



U. S. ENERGY CORP.                          TSUNAMI PARTNERS, L.P.



By:_____________________________            By:_________________________________
Name:    Keith G. Larsen                         Name:    Insue Kim
Title:   President                               Title:







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