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                                                                     EXHIBIT 4.1

              CERTIFICATE OF DESIGNATIONS, PREFERENCES AND RELATIVE
             PARTICIPATING OR OPTIONAL OR OTHER SPECIAL RIGHTS, AND
              QUALIFICATIONS, LIMITATIONS OR RESTRICTIONS THEREOF

                                       of

                       SERIES F REDEEMABLE PREFERRED STOCK

                                       of

                         AMERICAN REALTY INVESTORS, INC.

                       (Pursuant to Section 78.1955 of the
                            Nevada Revised Statutes)

     Pursuant to Section 78.1955 of the Nevada Revised Statutes ("NRS"), the
undersigned, being the Executive Vice President and Secretary, respectively, of
American Realty Investors, Inc, (the "Corporation"), Nevada corporation, hereby
certify that (a) the following resolution was duly adopted on May 17, 2001, by
the Board of Directors of the Corporation (the "Board"), for the purposes of
establishing a separate series of the Corporation's authorized preferred stock,
$2.00 par value ("Preferred Stock") and fixing the relative rights and
preferences of such series of Preferred Stock, and (b) such resolution has not
been subsequently modified or rescinded:

     RESOLVED, that in accordance with the provisions of Article Fourth of the
Articles of Incorporation of the Corporation, a series of Preferred Stock be,
and hereby is, created, and the voting powers, designations, preferences,
limitations, restrictions and relative, participating, optional or other special
rights of the shares of such series, and the qualifications, limitations or
restrictions thereof, be, and hereby are, as follows:

1.   Designation and Amount. The shares of such series shall be designated as
     ----------------------
     "Series F Redeemable Preferred Stock" (the "Series F Preferred Stock") and
     each share of the Series F Preferred Stock shall have a preference on
     liquidation as specified in Section 5 below. The number of shares
     constituting the Series F Preferred Stock shall be 4961. Such number of
     shares may be increased or decreased by the Board of Directors by filing an
     amendment to the Certificate of Designations, Preferences and Relative
     Participating or Optional or Other Special Rights, and Qualifications,
     Limitations or Restrictions Thereof to be filed with the Nevada Secretary
     of State in accordance with Section 78.1955 of NRS with respect to the
     Series F Preferred Stock ("Certificate of Designations") as provided in the
     Nevada Revised Statutes ("NRS"); provided, however, that no decrease shall
     reduce the number of shares of Series F Preferred Stock to a number less
     than the number of shares then outstanding plus the number of shares
     reserved for issuance upon the exercise of outstanding options, rights or
     warrants.

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2.   Dividends and Distributions. The holders of shares of Series F Preferred
     ---------------------------
     Stock shall not be entitled to receive any dividends or distributions
     except as provided in Section 5 hereof.

3.   Voting Rights and Powers. The holders of shares of Series F Preferred Stock
     ------------------------
     shall have only the following voting rights:

          (A) Except as may otherwise be specifically required by the NRS or
     otherwise specifically provided herein, the holders of the shares of Series
     F Preferred Stock shall not have the right to vote with respect to any such
     shares of stock, directly or indirectly, at any meeting of the shareholders
     of the Corporation or on any matter submitted to such shareholders for
     consent, and such shares of stock shall not be counted in determining the
     total number of outstanding shares to constitute a quorum at any meeting of
     shareholders;

          (B) In the event that, under the circumstances, the holders of the
     Series F Preferred Stock are entitled by law to vote upon any matter, the
     approval of such series shall be deemed to have been obtained only upon the
     affirmative vote or written consent of the holders of a majority of the
     shares of the Series F Preferred Stock then issued and outstanding;

          (C) Except as set forth herein, or as otherwise specifically provided
     by the Articles of Incorporation or the NRS, holders of the Series F
     Preferred Stock shall have no special voting rights and their consent shall
     not be required for the taking or authorization of any corporate action.

4.   Reacquired Shares. Any shares of Series F Preferred Stock purchased or
     -----------------
     otherwise acquired by the Corporation in any manner whatsoever shall no
     longer be deemed to be outstanding and all rights with respect to such
     shares of stock, including the right, if any, to receive notices and to
     vote, shall forthwith cease. All shares of Series F Preferred Stock
     acquired by the Corporation shall become authorized but unissued shares of
     Preferred Stock and may be reissued as part of a new series of Preferred
     Stock subject to the conditions and restrictions on issuance set forth
     herein, in the Articles of Incorporation, or in any other Certificates of
     Designations creating a series of Preferred Stock or any similar stock or
     as otherwise required by law.

5.   Liquidation, Dissolution or Winding Up. The Liquidation Value of the Series
     --------------------------------------
     F Preferred Stock shall be $1,000.00 per share. Upon any liquidation,
     dissolution or winding up of the Corporation, and after paying and
     providing for the payment of all creditors of the Corporation, the holders
     of shares of the Series F Preferred Stock then outstanding shall be
     entitled, before any distribution or payment is made upon any Junior
     Securities (which for the purposes of Sections 5 and 6 shall mean the
     Common Stock and any other equity security of any kind which the
     Corporation at any time has issued, issues or is authorized to issue if
     pursuant to the terms of such security the Series F Preferred Stock has
     priority thereover upon liquidation, dissolution or winding up of the
     Corporation), to receive a liquidation preference in an amount in cash
     equal to the Liquidation Value as of the date of such payment, whether such
     liquidation is voluntary or involuntary, and the holders of the Series

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     F Preferred Stock shall not be entitled to any other or further
     distributions of the assets of the Corporation. If, upon any liquidation,
     dissolution or winding up of the affairs of the Corporation, the net assets
     available for distribution to the holders of the Series F Preferred Stock
     and any shares of any other class or series of Preferred Stock which ranks
     on a parity with the Series F Preferred Stock on any such liquidation,
     dissolution or winding up shall be insufficient to permit payment to such
     holders of the aggregate amount to which they respectively shall be
     entitled, then the assets of the Corporation to be distributed to such
     holders will be distributed ratably among them based upon the amounts
     payable on the shares of each such series of Preferred Stock in the event
     of voluntary or involuntary liquidation, dissolution or winding up, as the
     case may be, in proportion to the full preferential amounts, together with
     any and all arrearages to which they are respectively entitled. Upon any
     such liquidation, dissolution or winding up of the Corporation, after the
     holders of the Series F Preferred Stock and shares of any other series of
     Preferred Stock which ranks on a parity with the Series F Preferred Stock
     on any such liquidation, dissolution or winding up have been paid in full
     the amounts to which they are entitled, the remaining assets of the
     Corporation may be distributed to holders of Junior Securities, including
     Common Stock, of the Corporation. The Corporation will mail written notice
     of such liquidation, dissolution or winding up, not less than twenty (20)
     nor more than fifty (50) days prior to the payment date stated therein to
     each record holder of Series F Preferred Stock. Neither the consolidation
     nor merger of the Corporation into or with any other corporation or
     corporations or business entities, nor the sale or transfer by the
     Corporation of less than all or substantially all of its assets, nor a
     reduction in the capital stock of the Corporation, nor the purchase or
     redemption by the Corporation of any shares of its Preferred Stock or
     Common Stock or any other class of its stock, nor the payment of any
     dividend in cash, securities or property on shares of the Common Stock or
     any Preferred Stock will be deemed to be a liquidation, dissolution or
     winding up of the Corporation within the meaning of this Section 5.

6.   Ranking. Except as provided in the following sentence, the Series F
     -------
     Preferred Stock shall rank on a parity upon liquidation, dissolution or
     winding up with all other shares of Preferred Stock issued by the
     Corporation. Unless the Corporation shall have called all remaining shares
     of the Series F Preferred Stock that are then outstanding for redemption,
     or shall have set aside a sufficient amount to permit such redemption, the
     Corporation shall not issue any shares of Preferred Stock of any series
     which are superior to the Series F Preferred Stock as to rights upon
     liquidation, dissolution or winding up of the Corporation as long as any
     shares of the Series F Preferred Stock are issued and outstanding, without
     the prior written consent of the holders of a majority of such shares of
     Series F Preferred Stock then outstanding voting separately as a class.

7.       Mandatory Redemptions.
         ---------------------

          (A) Quarterly Redemptions. From and after January 1,2002, Within ten
              ---------------------
     (10) calendar days of the filing by the Corporation of its Report on Form
     10-Q or Report on Form 10-K, each as promulgated under the Securities
     Exchange Act of 1934, as amended, or any

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     similar form promulgated under any successor statute thereto, with the
     Securities Exchange Commission, or any successor agency for public
     dissemination, the Corporation shall call for redemption that number of
     shares of the Series F Preferred Stock having an aggregate Liquidation
     Value equal to twenty percent (20%) of the Net Cash Flow (as subsequently
     defined) generated by the Assets during the preceding fiscal quarter (or,
     in the case of the first such filing, such shorter period as the Series F
     Preferred Stock shall have been outstanding) after payment of currently due
     payments of the (i) Operator's Note and (ii) Purchase Note. Shares of the
     Series F Preferred Stock redeemed pursuant to this Section 7 shall be
     redeemed for cash in accordance with the provisions of Section 8(B)-(D)
     below, except that the Corporation shall be obligated to redeem not less
     than the number of shares of Series F Preferred Stock required by the first
     sentence of this Section 7(A). Corporation shall deliver to MJR,
     contemporaneously with the making of each call for redemption pursuant to
     this Section 7(A), calculation of the Net Cash Flow for the preceding
     fiscal quarter.

          (B) Mandatory Redemptions. In the event that the Corporation shall
              ---------------------
     engage in a Fundamental Transaction (as subsequently defined), the
     Corporation shall, immediately prior to or contemporaneously with the
     consummation of any transaction constituting a Fundamental Change or giving
     rise to a Fundamental Change (and, in any case, contemporaneously with or
     prior to any distribution or payment made with respect to any Junior
     Securities), call for redemption each then outstanding share of Series F
     Preferred Stock at a price per share in cash equal to the Liquidation Value
     thereof. Any redemption pursuant to this Section 7(B) shall be made in
     accordance with the provisions of Section 8(B) below, except that the
     Corporation shall, in accordance with such provisions, call for redemption
     of each then outstanding share of the Series F Preferred Stock.

          (C) Definitions. For the purposes of this Section 7, the following
              -----------
     defined terms shall have the meanings set forth below:

               "Assets" means the Assets as defined in that certain Asset
          Purchase Agreement, dated as of May 30, 2001 between the Corporation
          and MJR Oil & Gas 2001, LLC.

               "Fundamental Transaction" means (a) any transfer of more than ten
          percent (10%) of the Assets (computed on the basis of the greater of
          (i) the Corporation's book value therein as determined in accordance
          with generally accepted accounting principles consistently applied or
          (ii) fair market value) in any transaction or series of related
          transactions, whether by sale of the Assets, merger, consolidation or
          reorganization of the Corporation or other business combination
          transaction, but excluding sales of oil, gas and minerals in the
          ordinary course of business, pledging of any of the Assets, the
          entering into of leases or the granting of licenses or rights of
          farm-in or farm-out or similar transactions customary in connection
          with the operation or development of oil and gas properties or the
          sale of oil, gas or other minerals produced therefrom and (b) any
          merger or consolidation to which the

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          Corporation is a party except for any merger pursuant to which the
          Corporation is the surviving business entity or one of the surviving
          business entities, the terms of the Series F Preferred Stock are not
          changed or altered in any respect, the Series F Preferred Stock is not
          exchanged for cash, securities or other property, and immediately
          after giving effect to such merger, the holders of the Common Stock
          immediately prior to such merger continue to own equity interest in
          the surviving business entity possessing the voting power at regular
          or special meetings of such equity holders or in connection with any
          consent solicited with regard thereto, to elect or otherwise designate
          a majority of the members of the Board of Directors or other governing
          body thereof under circumstances other than where the Corporation is
          in default of any obligation with respect to any shares of the
          Preferred Stock or any indenture, deed of trust or other agreement
          requiring disclosure as an exhibit on the Corporation's Report on Form
          10-K.

               "MJR" means MJR Oil & Gas 2001, LLC, a Texas limited liability
          company, and its successors and assigns.

               "Net Cash Flow" means for any period, (i) the gross receipts
          derived from the Assets for such period minus (ii) all costs and
          expenses actually incurred by the Corporation in the operation of the
          Assets for such period which are properly expensed under generally
          accepted accounting principles, including, but not limited to property
          taxes, insurance, operator's fees, landowner's royalty payments,
          utility expenses, maintenance costs, wages, benefits, repair, capital
          expenses determined to be necessary by the operator for production and
          all other costs of production, but not including (i) allocable
          corporate overhead costs, (ii) depreciation and amortization, (iii)
          and amounts expended for exploration; and provided, that any costs or
          expenses paid to the Corporation or an Affiliate of the Corporation
          shall be reduced to the amount that would actually be paid to an
          unaffiliated third party for equivalent products or services.

               "Operator's Note" shall have the meaning assigned such term in
          the Asset Purchase Agreement dated as of May 30, 2001, between the
          Corporation and MJR Oil & Gas 2001, LLC.

               "Purchase Note" shall have the meaning assigned such term in the
          Asset Purchase Agreement dated as of May 30, 2001, between the
          Corporation and MJR Oil & Gas 2001, LLC.

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8.   Redemption at the Option of the Corporation.
     -------------------------------------------

          (A) The Corporation shall have the right to redeem all or a portion of
     the Series F Preferred Stock issued and outstanding at any time and from
     time to time, at its option, for cash. The redemption price of the Series F
     Preferred Stock pursuant to this Section 8 shall be an amount per share
     equal to the Liquidation Value (the "Redemption Price").

          (B) The Corporation may redeem all or a portion of any holder's shares
     of Series F Preferred Stock by giving such holder not less than 20 days nor
     more than 30 days notice thereof prior to the date on which the Corporation
     desires such shares to be redeemed, which date (the "Redemption Date")
     shall be a day upon which banks are not required to be closed in Dallas,
     Texas (a "Business Day"). Such notice shall be written and shall be hand
     delivered or mailed, postage prepaid, to the holder (the "Redemption
     Notice"). If mailed, such notice shall be deemed to be delivered when
     deposited in the United States Mail, postage prepaid, addressed to the
     holder of shares of Series F Preferred Stock at his address as it appears
     on the stock transfer records of the Corporation. The Redemption Notice
     shall state (i) the total number of shares of Series F Preferred Stock held
     by such holder; (ii) the total number of shares of the holder's Series F
     Preferred Stock that the Corporation intends to redeem; (iii) the
     Redemption Date and the Redemption Price; and (iv) the place at which the
     holder(s) may obtain payment of the applicable Redemption Price upon
     surrender of the share certificate(s).

          (C) If fewer than all shares of the Series F Preferred Stock at any
     time outstanding shall be called for redemption, such shares shall be
     redeemed pro rata from among the record holders of the Series F Preferred
     Stock based upon the aggregate Liquidation Value represented by shares, and
     fractional shares, held. Fractional shares of the Series F Preferred Stock
     may be redeemed.

          (D) If a Redemption Notice shall have been so mailed, at least two
     Business Days prior to the Redemption Date the Corporation shall provide
     for payment of a sum sufficient to redeem the applicable number of shares
     of Series F Preferred Stock subject to redemption either by (i) setting
     aside the sum required to be paid as the Redemption Price by the
     Corporation, separate and apart from its other funds, in trust for the
     account of the holder(s) of the shares of Series F Preferred Stock to be
     redeemed or (ii) depositing such sum in a bank or trust company (either
     located in the state where the principal executive office of the
     Corporation is maintained, such bank or trust company having a combined
     surplus of at least $20,000,000 according to its latest statement of
     condition, or such other bank or trust company as may be permitted hereby
     or by law) as a trust fund, with irrevocable instructions and authority to
     the bank or trust company to give or complete the notice of redemption and
     to pay, on or after the Redemption Date, the applicable Redemption Price on
     surrender of certificates evidencing the Redemption Date, the applicable
     Redemption Price on surrender of certificates evidencing the share(s) of
     Series F Preferred Stock so called for redemption and, in either event,
     from and after the Redemption Date (v) the share(s) of Series F Preferred
     Stock shall be deemed to be redeemed, (w) such setting aside or deposit
     shall be deemed to constitute full payment for such share(s), (x) such
     share(s) so redeemed shall no longer be

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     deemed to be outstanding, (y) the holder(s) thereof shall cease to be a
     stockholder of the Corporation with respect to such share(s), and (z) such
     holder(s) shall have no rights with respect thereto except the right to
     receive the Redemption Price for the applicable shares. Any interest on the
     funds so deposited shall be paid to the Corporation. Any and all such
     redemption deposits shall be irrevocable except to the following extent:
     any funds deposited which shall not be required for the redemption of any
     shares of Series F Preferred Stock because of any prior acquisition or
     purchase by the Corporation other than through the redemption process,
     subsequent to the date of deposit but prior to the Redemption Date, shall
     be repaid to the Corporation forthwith and any balance of the funds so
     deposited and unclaimed by the holder(s) of any shares of Series F
     Preferred Stock entitled thereto at the expiration of one calendar year
     from the Redemption Date shall be repaid to the Corporation upon its
     request or demand therefor, and after any such repayment of the holder(s)
     of the share(s) so called for redemption shall look only to the Corporation
     for payment of the Redemption Price thereof. All shares of Series F
     Preferred Stock redeemed shall be restored to the status of authorized but
     unissued shares of Preferred Stock.

          (E) Holders whose shares have been redeemed hereunder shall surrender
     the certificate or certificates representing such shares, duly endorsed or
     assigned (unless such endorsement or assignment be waived by the
     Corporation), to the Corporation by mail, courier or personal delivery at
     the Corporation's principal executive office or other location so
     designated in the Redemption Notice, and upon the Redemption Date the
     Redemption Price shall be payable to the order of the person whose name
     appears on such certificate or certificates as the owner thereof, and each
     surrendered certificate shall be canceled and retired. In the event fewer
     than all of the shares represented by such certificates are redeemed, a new
     certificate shall be issued representing the unredeemed shares.

9.   Sinking Fund. The Corporation shall not be required to maintain any
     ------------
     so-called "sinking fund" for the retirement on any basis of the Series F
     Preferred Stock.

10.  Fractional Shares. The Series F Preferred Stock may be issued in fractions
     -----------------
     of a share which shall entitle the holder, in proportion to such holder's
     fractional shares, to have the benefit of all other rights of holders of
     shares of Series F Preferred Stock.

11.  Notice. Any notice or request made to the Corporation in connection with
     ------
     the Series F Preferred Stock shall be given, and shall conclusively be
     deemed to have been given and received three Business Days following
     deposit thereof in writing, in the U.S. mails, certified mail, return
     receipt requested, duly stamped and addressed to the Corporation, to the
     attention of its General Counsel, at its principal executive offices (which
     shall be deemed to be the address most recently provided to the Securities
     and Exchange Commission ("SEC") as its principal executive offices for so
     long as the Corporation is required to file reports with the SEC).

12.  Registration and Transfer. The Corporation shall maintain a register for
     -------------------------
     the registration of the Series F Preferred Stock. Upon the surrender of any
     certificate representing Series F Preferred Stock, properly endorsed and
     having such other evidence of proper transfer under

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     applicable law as the Corporation may reasonably require, the Corporation
     shall, at the request of the record holder of such certificate, execute and
     deliver (at the Corporation's expense) a new certificate or certificates in
     exchange therefor. Each such certificate shall be registered in such name
     and shall represent such number of shares as is requested by the holder of
     the surrendered certificate and shall be substantially identical in form to
     the surrendered certificate.

13.  Replacement. Upon receipt of evidence reasonably satisfactory to the
     -----------
     Corporation the loss, theft, destruction or mutilation of any certificate
     evidencing shares of the Series F Preferred Stock by the record holder
     thereof, together with an indemnity and other security (such as a lost
     instruments bond) reasonably satisfactory to the Corporation, or in the
     case of mutilation, upon the surrender of such certificate, the Corporation
     shall (at its expense) execute and deliver in lieu of such lost, stolen,
     destroyed or mutilated certificate a new certificate of like kind
     representing the number of shares of the Series F Preferred Stock
     represented thereby.

14.  Amendment Waiver. The provisions of the Certificate of Designations may be
     ----------------
     amended, and any obligation of the Corporation provided for thereunder may
     be waived, upon the affirmative vote or written consent of holders of a
     majority of the then outstanding shares of Series F Preferred Stock.

     IN WITNESS WHEREOF, these Articles of Amendment are executed on behalf of
the Corporation by its Executive Vice President and attested by its Secretary as
of the 11th day of June, 2001.

                                                    /s/ Louis J. Corna
                                               ---------------------------------
                                               Louis J. Corna
                                               Executive Vice President

Attest:   /s/ Robert A. Waldman
       ----------------------------
       Robert A. Waldman
       Secretary


STATE OF TEXAS             )
                           ) ss
COUNTY OF DALLAS           )

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     This instrument was acknowledged before me on June 11, 2001, by Louis J.
Corna as Executive Vice President of American Realty Investors, Inc., a Nevada
corporation.

                                                 /s/ S.L. Bratton
                                               -------------------------------
                                               Notary Public
                                               My Commission Expires:  9-25-04
                                                                     -----------

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