<PAGE>   1



                                                                     EXHIBIT 3.1


                           CERTIFICATE OF DESIGNATION

                                       of

                     TRANSCONTINENTAL REALTY INVESTORS, INC.

                                setting forth the

       VOTING POWERS, DESIGNATIONS, PREFERENCES, LIMITATIONS, RESTRICTIONS
                               AND RELATIVE RIGHTS

                                       of

                 SERIES A CUMULATIVE CONVERTIBLE PREFERRED STOCK

                         (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 President and Secretary, respectively, of
Transcontinental Realty Investors, Inc. (the "Corporation"), a Nevada
corporation, hereby certify that (a) the following resolution was duly adopted
on October 20, 1998, 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, $0.01 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resolution has not been subsequently modified or rescinded: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:

Section 1. Designation and Amount. The shares of such series shall be designated
as "Series A Cumulative Convertible Preferred Stock" (the "Series A Stock") and
each share of the Series A Stock shall have a par value of $0.01 per share and a
preference on liquidation as specified in Section 6 below. The number of shares
constituting the Series A Stock shall be 6,000. Such number of shares may be
increased or decreased by the Board by filing an amendment to this Certificate
of Designation, provided, however, that no decrease shall reduce the number of
shares of Series A 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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<PAGE>   2







Section 2.       Dividends and Distributions.

     (A) The holders of Series A Stock shall be entitled to receive, when, as,
and if declared by the Board and to the extent permitted under the NRS, out of
funds legally available for the purpose and in preference to and with priority
over dividends upon all Junior Securities (as defined in Section 6 below),
quarterly cumulative dividends payable in arrears in cash on the tenth day
following the end of each calendar quarter, unless such day is a Saturday,
Sunday or holiday, in which case such dividends shall be payable on the next
succeeding business day (each such date being referred to herein as a "Quarterly
Dividend Payment Date"), commencing on the first Quarterly Dividend Payment Date
after the first issuance of a share or fraction of a share of Series A Stock, in
an amount per share (rounded to the next highest cent) equal to 5% per annum of
the Liquidation Value (as defined in Section 6 below), as determined immediately
prior to the beginning of such calendar quarter assuming each year consists of
360 days and each quarter consists of 90 days.

     (B) Dividends shall commence accruing cumulatively on outstanding shares of
the Series A Stock from the date of issuance of such shares to and including the
date on which the Redemption Price (as defined in Section 9(A) below) of such
shares is paid, whether or not such dividends have been declared and whether or
not there are profits, surplus or other funds of the Corporation legally
available for the payment of such dividends. For purposes of this Section 2, the
date on which the Corporation has issued any share of Series A Stock is its date
of issuance, regardless of the number of times a transfer of such share is made
on the stock records maintained by or for the Corporation and regardless of the
number of certificates that may be issued to evidence such share (whether by
reason of transfer of such share or for any other reason). Dividends paid on the
shares of Series A Stock in an amount less than the total amount of dividends at
the time accrued and payable on such shares shall be allocated among the holders
of such shares in proportion to their respective Unpaid Accrual Amounts, where
for this purpose the "Unpaid Accrual Amount" of a holder of shares of Series A
Stock at any time equals the total of accrued unpaid dividends on all such
shares held by such holder. The Board may fix a record date for the
determination of holders of shares of Series A Stock entitled to receive payment
of a dividend or distribution declared thereon other than a quarterly dividend
paid on the Quarterly Dividend Payment Date immediately after such dividend
accrued, which record date shall be not more than fifty (50) days prior to the
date fixed for the payment thereof.

     (C) So long as any shares of the Series A Stock are outstanding, the
Corporation will not make, directly or indirectly, any distribution (as such
term is defined in the NRS) with respect to Junior Securities unless, on the
date specified for measuring such distribution, (a) all accrued dividends on the
Series A Stock for all past quarterly dividend periods have been paid in full
and the full amount of accrued dividends for the then current quarterly dividend
period has been paid or declared and a sum sufficient for the payment thereof
set apart and (b) after giving effect to such distribution (i) the Corporation
would not be rendered unable to pay its debts as they become due in the usual
course of business; and (ii) the Corporation's total assets would not be less
than the sum of its total liabilities plus the amount that would be needed, if
the Corporation were to be dissolved at the time of the distribution, to satisfy
the preferential rights upon






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<PAGE>   3



dissolution of the holders of the Series A Stock as provided in this Certificate
of Designation. Dividends shall not be paid (in full or in part) or declared and
set apart for payment (in full or in part) on any series of Preferred Stock
(including the Series A Stock) for any dividend period unless all dividends, in
the case dividends are being paid in full on the Series A Stock, or a ratable
portion of all dividends (i.e., so that the amount paid on each share of each
series of Preferred Stock as a percentage of total accrued and unpaid dividends
for all periods with respect to each such share is equal), in the case dividends
are not being paid in full on the Series A Stock, have been or are,
contemporaneously, paid and declared and set apart for payment on all
outstanding series of Preferred Stock (including the Series A Stock) entitled
thereto for each dividend period terminating on the same or earlier date. If at
any time the Corporation pays less than the total amount of dividends then
accrued with respect to the Series A Stock, such payment will be distributed
ratably among the then holders of Series A Stock so that an equal amount is paid
with respect to each outstanding share.

Section 3.       Conversion Rights.

     (A) The Series A Stock may be converted at any time and from time to time
in whole or in part after November 1, 2003, at the option of the holders
thereof, in accordance with subsection (D) below at the Conversion Price (as
defined in subsection (B) below) into fully paid and nonassessable shares of
common stock, $.01 par value, of the Corporation ("Common Stock"). The number of
shares of Common Stock to be issued pursuant to such conversion shall be equal
to the number of shares offered for conversion multiplied by the Liquidation
Value per share and divided by the Conversion Price; provided, however, that (1)
as to any shares of Series A Stock which shall have been called for redemption
pursuant to Section 9, the right of conversion shall terminate upon receipt by
the holder of the notice of redemption from the Corporation and (2) on the
earlier of (a) the commencement of any liquidation, dissolution or winding up of
the Corporation by the filing with the Secretary of State of the State of Nevada
or with a federal bankruptcy court or (b) the adoption by the stockholders of
the Corporation of any resolution authorizing the commencement thereof, the
right of conversion shall terminate. Notwithstanding anything to the contrary
herein provided, the Corporation may elect to redeem the shares of Series A
Stock sought to be converted, pursuant to Section 9 hereunder, instead of
issuing shares of Common Stock in replacement thereof, in accordance with the
provisions of Section 3(D) below.

     (B) For purposes of this Section 3, the term "Conversion Price" shall be
and mean the simple average of the daily closing price of the Common Stock for
the closing sale price for the five (5) Business Days immediately prior to the
date of conversion on the New York Stock Exchange or, if the Common Stock is not
then being traded on the New York Stock Exchange, then on the principal stock
exchange (including without limitation The Nasdaq Stock Market) on which the
Common Stock is then listed or admitted to trading as determined by the
Corporation ("Principal Stock Exchange") or, if the Common Stock is not then
listed or admitted to trading on a Principal Stock Exchange, the average of the
last reported closing bid and asked prices on such days in the over-the-counter
market or, if no such prices are available, the fair market value per share of
the Common Stock, as determined by the Board in its sole discretion. The
Conversion Price shall not be subject to any adjustment as a result of the
issuance of any additional shares of Common






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Stock by the Corporation for any purpose, except for stock splits (whether
accomplished by stock dividends or otherwise) or reverse stock splits occurring
during the five (5) Business Days referenced in the calculation of the
Conversion Price. For purposes of calculating the Conversion Price, the term
"Business Day" shall mean a day on which the Principal Stock Exchange is open
for business or, if no such exchange, the term "Business Day" shall have the
meaning given such term in Section 3(D) below.

     (C) Upon any conversion, fractional shares of Common Stock shall not be
issued but any fractions shall be adjusted by the delivery of one additional
share of Common Stock in lieu of any cash. Any accrued but unpaid dividends
shall be convertible into shares of Common Stock as provided for in this
Section. The Corporation shall pay all issue taxes, if any, incurred in respect
to the issuance of Common Stock on conversions, provided, however, that the
Corporation shall not be required to pay any transfer or other taxes incurred by
reason of the issuance of such Common Stock in names other than those in which
the Series A Stock surrendered for conversion may stand.

     (D) Any conversion of Series A Stock into Common Stock shall be made by the
surrender to the Corporation, at the office of the Corporation set forth in
Section 11 hereof or at the office of the transfer agent for such shares, of the
certificate or certificates representing the Series A Stock to be converted,
duly endorsed or assigned (unless such endorsement or assignment be waived by
the Corporation) together with a written request for conversion. The Corporation
shall either (i) issue as of the date of receipt by the Corporation of such
surrender shares of Common Stock calculated as provided above and evidenced by a
stock certificate delivered to the holder as soon as practicable after the date
of such surrender; or (ii) within two (2) Business Days (unless otherwise
provided, "Business Day" herein shall mean any day other than a Saturday, a
Sunday or a day on which banking institutions in Dallas, Texas are authorized or
obligated by law or executive order to remain closed) after the date of such
surrender advise the holder of the Series A Stock that the Corporation is
exercising its option to redeem the Series A Stock pursuant to Section 9, in
which case the Corporation shall have sixty (60) days from the date of such
surrender to pay to the holder cash in an amount equal to the Redemption Price
(as defined in Section 9(A) below) for each share of Series A Stock so redeemed.
The date of surrender of any Series A Stock shall be the date of receipt by the
Corporation or its agent of such surrendered shares of Series A Stock.

     (E) A number of authorized shares of Common Stock sufficient to provide for
the conversion of the Series A Stock outstanding upon the basis hereinbefore
provided shall at all times be reserved for such conversion. If the Corporation
shall propose to issue any securities or to make any change in its capital
structure which would change the number of shares of Common Stock into which
each share of Series A Stock shall be convertible as herein provided, the
Corporation shall at the same time also make proper provision so that thereafter
there shall be a sufficient number of shares of Common Stock authorized and
reserved for conversion of the outstanding Series A Stock on the new basis.








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     (F) In case the Corporation shall propose at any time before all shares of
the Series A Stock have been redeemed by the Corporation or converted into
Common Stock:

         (i)   to pay any dividend on the Common Stock outstanding payable in
     Common Stock or to make any other distribution, other than cash dividends
     to the holders of the Common Stock outstanding; or

         (ii)  to offer for subscription to the holders of the Common Stock
     outstanding any additional shares of any class or any other rights or
     option; or

         (iii) to effect any re-classification or recapitalization of the 
     Common Stock outstanding involving a change in the Common Stock, other 
     than a subdivision or combination of the Common Stock outstanding; or

         (iv)  to merge or consolidate with or into any other corporation 
     (unless the Corporation is the surviving entity and holders of Common Stock
     continue to hold such Common Stock without modification and without receipt
     of any additional consideration), or to sell, lease, or convey all or
     substantially all its property or business, or to liquidate, dissolve or
     wind up;

then, in each such case, the Corporation shall mail to the holders of record of
each of the shares of Series A Stock at their last known address as shown by the
Corporation's records a statement, signed by an officer of the Corporation, with
respect to the proposed action. Such statement shall be so mailed at least
thirty (30) days prior to the date of the taking of such action or the record
date for holders of the Common Stock for the purposes thereof, whichever is
earlier. If such statement relates to any proposed action referred to in clauses
(iii) or (iv) of this subsection (G), it shall set forth such facts with respect
thereto as shall reasonably be necessary to inform the holders of the Series A
Stock as to the effect of such action upon the conversion rights of such
holders.

Section 4.   Voting Rights and Powers.  The holders of shares of Series A Stock
shall have only the following voting rights:

         (A) Except as may otherwise be specifically required by law or
     otherwise provided herein, the holders of the shares of Series A Stock
     shall not have the right to vote such stock, directly or indirectly, at any
     meeting of the stockholders of the Corporation, 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 stockholders.

         (B) In the event that, under the circumstances, the holders of the
     Series A Stock are required by law to vote upon any matter, the approval of
     such series shall be deemed to have been obtained only upon the affirmative
     vote of the holders of a majority of the shares of the Series A Stock then
     outstanding.





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

Section 5. Reacquired Shares. Any shares of Series A Stock purchased or
otherwise acquired by the Corporation in any manner whatsoever or surrendered
for conversion hereunder 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, shall forthwith cease except, in the case of stock surrendered
for conversion hereunder, rights of the holders thereof to receive Common Stock
in exchange therefor. All shares of Series A Stock obtained by the Corporation
shall be retired and canceled promptly after the acquisition thereof. All such
shares shall upon their cancellation 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.

Section 6. Liquidation, Dissolution or Winding Up. The Liquidation Value of the
Series A Stock shall be $100.00 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 A Stock
then outstanding shall be entitled, before any distribution of payment is made
upon the Common Stock and any other equity security of any kind, other than
Preferred Stock, which the Corporation at any time has issued, issues or is
authorized to issue (collectively, "Junior Securities"), to receive a
liquidation preference in an amount in cash equal to the Adjusted Liquidation
Value as of the date of such payment, whether such liquidation is voluntary or
involuntary, and the holders of the Series A Stock shall not be entitled to any
other or further distributions of the assets. If, upon any liquidation,
dissolution or winding up of the affairs of the Corporation, the net assets
available for distribution shall be insufficient to permit payment to the
holders of all outstanding shares of all series of Preferred Stock of the 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
Preferred Stock 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 A Stock. Neither the consolidation nor
merger of the Corporation with or into any other corporation or corporations,
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 will be deemed to be a
liquidation, dissolution or winding up of the Corporation within the meaning of
this Section





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6. "Adjusted Liquidation Value" shall mean the Liquidation Value as defined in
this Section 6 plus all accrued and unpaid dividends through the applicable
date.

Section 7. Ranking. Except as provided in the following sentence, the Series A
Stock shall rank on parity as to dividends and upon liquidation, dissolution or
winding up with all other shares of Preferred Stock issued by the Corporation.
The Corporation shall not issue any shares of Preferred Stock of any series
which are superior to the Series A Stock as to dividends or rights upon
liquidation, dissolution or winding up of the Corporation as long as any shares
of the Series A Stock are issued and outstanding without the prior written
consent of the holders of at least a majority of such shares of Series A Stock
then outstanding voting separately as a class.

Section 8. Redemption at the Option of the Holder. The shares of Series A Stock
shall not be redeemable at the option of a holder of Series A Stock.

Section 9. Redemption at the Option of the Corporation.

         (A) In addition to the redemption right of the Corporation set forth in
     Section 3(A), above, the Corporation shall have the right to redeem all or
     a portion of the Series A Stock issued and outstanding at any time and from
     time to time, at its option, for cash. The redemption price of the Series A
     Stock pursuant to this Section 9 shall be an amount per share equal to the
     Adjusted Liquidation Value as of the Redemption Date (the "Redemption
     Price").

         (B) The Corporation may redeem all or a portion of any holder's shares
     of Series A Stock by giving such holder not less than twenty (20) days nor
     more than thirty (30) days notice thereof prior to the date on which the
     Corporation desires such shares to be redeemed, which date shall be a
     Business Day (the "Redemption Date"). Such notice shall be in writing 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 A Stock at his address as it
     appears on the stock transfer records of the Corporation. The right of the
     Corporation to redeem shares of Series A Stock shall remain effective
     notwithstanding prior receipt by the Corporation of notice by any holder of
     Series A Stock of such holder's intent to convert shares of Series A Stock
     in accordance with Section 3 above, provided that the Redemption Notice is
     given on or prior to the second Business Day following the date of
     surrender of shares made to convert said shares to Common Stock. The
     Redemption Notice shall state (i) the total number of shares of Series A
     Stock held by such holder; (ii) the total number of shares of the holder's
     Series A 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).





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         (C) If fewer than all shares of the Series A Stock at any time
     outstanding shall be called for redemption, such shares shall be redeemed
     pro rata, by lot drawn or other manner deemed fair in the sole discretion
     of the Board to redeem one or more such shares without redeeming all such
     shares of Series A Stock. If a Redemption Notice shall have been so mailed,
     at least two (2) 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 A 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 A 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 by the Articles of
     Incorporation, 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 share(s) of
     Series A Stock so called for redemption and, in either event, from and
     after the Redemption Date (a) the share(s) of Series A Stock shall be
     deemed to be redeemed; (b) such setting aside or deposit shall be deemed to
     constitute full payment for such share(s); (c) such share(s) so redeemed
     shall no longer be deemed to be outstanding; (d) the holder(s) thereof
     shall cease to be a stockholder of the Corporation with respect to such
     share(s); and (e) 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 so deposited which shall not be required for
     the redemption of any shares of Series A Stock because of any prior sale 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 A 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 A Stock redeemed shall be
     canceled and retired and no shares shall be issued in place thereof, but
     such shares shall be restored to the status of authorized but unissued
     shares of Preferred Stock.

         (D) Holders whose shares of Series A Stock 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





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<PAGE>   9




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.

Section 10. Sinking Fund.  The Corporation shall not be required to maintain 
any so-called "sinking fund" for the retirement on any basis of the Series A
Stock.

Section 11. Notice. Any notice or request made to the Corporation in connection
with the Series A Stock shall be given in writing, and shall conclusively be
deemed to have been given and received three (3) Business Days following deposit
thereof, 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).

     IN WITNESS WHEREOF, this Certificate of Designation is executed on behalf
of the Corporation by its President and its Secretary as of the 30th day of
October, 1998.



                                                 /s/ Randall M. Paulson
                                                 -----------------------------
                                                 Randall M. Paulson, President


                                                 /s/ Thomas A. Holland
                                                 -----------------------------
                                                 Thomas A. Holland, Secretary


STATE OF TEXAS      )
                    )
COUNTY OF DALLAS    )

     This instrument was acknowledged before me on October 30, 1998 by Randall
M. Paulson.

                                                 /s/ S. L. Bratton
                                                 -----------------------------
                                                 Notary Public, State of Texas







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