Exhibit 4.1

                         PARALLEL PETROLEUM CORPORATION
               CERTIFICATE OF DESIGNATIONS, PREFERENCES AND RIGHTS
                           OF SERIAL PREFERRED STOCK -
                         6% CONVERTIBLE PREFERRED STOCK


                     Pursuant to Section 151 of the Delaware
                             General Corporation Law


         Pursuant to the provisions of Section 151 of the General Corporation
Law of the State of Delaware and Paragraph Fourth of the Certificate of
Incorporation of Parallel Petroleum Corporation (the "Company"), the undersigned
Company submits the following statement for the purpose of establishing and
designating a series of shares and fixing and determining the relative rights
and preferences thereof:

         1. The name of the corporation is Parallel Petroleum Corporation.

         2. The following resolutions were duly adopted by the Board of
Directors of the Company on October 13, 1998:

         WHEREAS, the Company is authorized by its Certificate of Incorporation,
as amended, to issue 10,000,000 shares of Preferred Stock, $.10 par value; and

         WHEREAS, the Certificate of Incorporation does not otherwise state or
fix the designations, preferences, voting rights and relative, participating,
optional or other special rights, qualifications, limitations and restrictions
of the preferred stock, $.10 par value, of the Company, but instead authorizes
the issuance thereof in series from time to time with such designations,
preferences, voting rights, rights of conversion into Common Stock and relative,
participating, optional or other rights, qualifications, limitations and
restrictions thereof as shall be stated and expressed in the resolution or
resolutions providing for the creation and issuance of such series adopted by
the Board of Directors of the Company; and

         WHEREAS, the Board of Directors deems it advisable to create and
establish and authorize the issuance of a new series of the Company's preferred
stock, $.10 par value;

         NOW, THEREFORE, BE IT RESOLVED, by the Board of Directors of the
Company, that pursuant to authority expressly granted to and vested in the Board
of Directors by the provisions of the Certificate of Incorporation of the
Company,


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the Board of Directors hereby creates a series of the class of authorized Serial
Preferred Stock, $.10 par value ("Preferred Stock"), of the Company, and
authorizes the issuance thereof, and hereby fixes the designations and amount
thereof, and the voting powers, preferences and relative, participating,
optional and other special rights of the shares of such series, and the
qualifications, limitations or restrictions thereof (in addition to the
designations, preferences and relative, participating and other special rights,
and the qualifications, limitations or restrictions thereof, set forth in the
Certificate of Incorporation of the Company, which are applicable to the Serial
Preferred Stock of all series) as follows:

         1.1 Designation and Amount. The shares of such series shall be
designated "6% Convertible Preferred Stock" (such series being hereinafter
sometimes called "this Series"), and the number of shares constituting such
Series shall initially be 1,200,000. The Board of Directors of the Company
reserves the right by subsequent amendment of this resolution from time to time
to decrease the number of shares which constitute this Series (but not below the
number of shares thereof then outstanding) and, subject to anything to the
contrary set forth in the Certificate of Incorporation of the Company applicable
to the preferred stock, to subdivide the number of shares, the stated value per
share and the liquidation value per share of this Series and in other respects
to amend, within the limitations provided by law, this resolution and the
Certificate of Incorporation of the Company.

         1.2 Dividends. The holders of shares of this Series shall be entitled
to receive, out of the funds of the Company legally available therefor and as
and when declared by the Board of Directors, cash dividends at the rate of $.60
per share per annum, payable semi-annually on the fifteenth day of the months of
June and December in each year, commencing December 15, 1998, except that if
such date is a Saturday, Sunday or legal holiday then such dividend shall be
payable on the first immediately preceding day which is not a Saturday, Sunday
or legal holiday. Such dividends shall be cumulative (whether or not in any
semi-annual dividend period there shall be funds of the Company legally
available for the payment of such dividends), commencing on the date of original
issue and shall be payable for any period less than a full semi-annual period on
the basis of a year of 360 days with equal 30 day months. Dividends shall be
payable to holders of record, as they appear on the stock books of the Company
on such record dates as may be declared by the Board of Directors, not more than
sixty (60) days nor less than ten (10) days preceding the payment dates for such
dividends. Dividends in arrears may be declared and paid at any time, without
reference to any regular dividend payment date, to holders of record on such
date, not exceeding sixty (60) days preceding the payment date thereof, as may
be fixed by the Board of Directors of the Company. Except as provided below with
regard

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to any class of stock ranking on a parity with the Preferred Stock as to payment
of dividends, in no event, so long as this Series shall remain outstanding,
shall any dividend whatsoever be declared or paid upon, nor shall any
distribution be made or ordered in respect of, any class of stock of the Company
ranking on a parity with or junior to this Series with respect to payment of
dividends, unless dividends on this Series since the date of issue thereof to
the date of such distribution shall have been paid or declared and set apart for
payment. When dividends are not paid in full upon the shares of this Series and
any other preferred stock ranking on a parity as to payment of dividends with
this Series, all dividends declared upon shares of this Series and any other
preferred stock ranking on a parity as to dividends with this Series shall be
declared pro rata so that the amount of dividends declared per share on this
Series and such other preferred stock shall in all cases bear to each other the
same ratio that accrued dividends per share on the shares of this Series and
such other preferred stock bear to each other. If full cumulative dividends on
this Series have not been declared and paid or set apart for payment, the
Company shall not declare or pay or set apart for payment any dividends or make
any other distributions on, or make any payment on account of the purchase,
redemption or retirement of, the Common Stock, $.01 par value, of the Company
("Common Stock"), or any other stock of the Company ranking junior to this
Series as to dividends or distribution of assets on liquidation, dissolution or
winding up of the Company (other than, in the case of dividends or
distributions, dividends or distributions paid in shares of Common Stock or such
other junior ranking stock), until full cumulative dividends on this Series are
declared and paid or set apart for payment.

         1.3 Conversion. The holders of shares of this Series shall have the
right, at their option, to convert all or any part of such shares of this Series
into shares of Common Stock of the Company at any time after April 20, 1999 and
subject to the following terms and conditions:

                  (a) The shares of this Series shall be convertible at the
          office of any transfer agent for such stock, and at such other place
          or places, if any, as the Board of Directors of the Company may
          designate, into fully paid and nonassessable shares (calculated as to
          each conversion to the nearest 1/100th of a share) of Common Stock of
          the Company. The number of shares of Common Stock issuable upon
          conversion of each share of this Series shall be equal to $10.00
          divided by the conversion price in effect at the time of conversion,
          determined as hereinafter provided. The price at which shares of
          Common Stock shall be delivered upon conversion (herein called the
          "conversion price") shall be initially $3.50 per share of Common
          Stock. The conversion price shall be subject to adjustment from time
          to time in certain instances as hereinafter provided. If the Company
          calls for

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          the redemption of any shares of this Series, such right of conversion
          shall cease and terminate, as to the shares designated for redemption,
          at the close of business on the redemption date, unless the Company
          defaults in the payment of the redemption price. No fractional shares
          of Common Stock will be issued. A cash payment will be paid in lieu of
          any fractional share in an amount equal to the same fraction of the
          last sale price of the Common Stock (determined as provided in Section
          1.3(c)(iv)) at the close of business on the business day which next
          precedes the day of conversion.

                  (b) Before any holder of shares of this Series shall be
          entitled to convert the same into Common Stock, he shall surrender the
          certificate or certificates therefor, duly endorsed or assigned to the
          Company or in blank, at the office of any transfer agent for such
          stock or at such other place or places, if any, as the Board of
          Directors of the Company may have designated, and shall give written
          notice to the Company at said office or place that he elects to
          convert the same and shall state in writing therein the name or names
          (with addresses) in which he wishes the certificate or certificates
          for Common Stock to be issued. Shares of this Series surrendered for
          conversion during the period from the close of business on any record
          date for the payment of a dividend on the shares of this Series to the
          opening of business on the date for payment of such dividends shall
          (except in the case of shares of this Series which have been called
          for redemption on a redemption date within such period) be accompanied
          by payment of an amount equal to the dividend payable on such dividend
          payment date on the shares of this Series being surrendered for
          conversion. Except as provided in the preceding sentence, no payment
          or adjustment shall be made upon any conversion on account of any
          dividend accrued on the shares of this Series surrendered for
          conversion or on account of any dividends on the Common Stock issued
          upon conversion. The Company will, as soon as practicable thereafter,
          issue and deliver at said office or place to such holder of shares of
          this Series, or to his nominee or nominees, certificates for the
          number of full shares of Common Stock to which he shall be entitled as
          aforesaid, together with cash in lieu of any fraction of a share.
          Shares of this Series shall be deemed to have been converted as of the
          close of business on the date of surrender of such shares for
          conversion as provided above, and the person or persons entitled to
          receive the Common Stock issuable upon such conversion shall be
          treated for all purposes as the record holder or holders of such
          Common Stock as of the close of business on such date.

                  (c) The conversion price in effect at any time shall be
          subject to adjustment as follows:


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                           (i) In case the Company shall (A) declare a dividend
                  or make a distribution payable in Common Stock on any class of
                  capital stock of the Company, unless the payment thereof would
                  increase the number of shares of Common Stock outstanding by
                  less than one percent (1%), (B) subdivide or reclassify its
                  outstanding shares of Common Stock into a greater number of
                  shares, or (C) combine its outstanding shares of Common Stock
                  into a smaller number of shares, the conversion price in
                  effect at the time of the record date for such dividend or
                  distribution or the effective date of such subdivision,
                  combination or reclassification shall be proportionately
                  reduced in the case of any increase in the number of shares of
                  Common Stock outstanding and increased in the case of any
                  reduction in the number of shares of Common Stock outstanding
                  so that the holder of any share of this Series surrendered for
                  conversion after such time shall be entitled to receive the
                  kind and amount of shares which he would have owned or have
                  been entitled to receive had such share of this Series been
                  converted into Common Stock immediately prior to such time and
                  had such Common Stock received such dividend or other
                  distribution or participated in such subdivision, combination
                  or reclassification. Such adjustment shall be effective as of
                  the record date for such dividend or distribution or the
                  effective date of such combination, subdivision or
                  reclassification and shall be made successively whenever any
                  event listed above shall occur.

                           (ii) In case the Company shall issue rights or
                  warrants to all holders of its Common Stock entitling them to
                  subscribe for or purchase shares of Common Stock at a price
                  per share less than the Current Market Price (as defined in
                  paragraph (iv) below) of the Common Stock, on the date fixed
                  for the determination of stockholders entitled to receive such
                  rights or warrants, the conversion price at the opening of
                  business on the day following the date fixed for such
                  determination shall be reduced by multiplying the conversion
                  price by a fraction of which the numerator shall be the number
                  of shares of Common Stock outstanding at the close of business
                  on the date fixed for such determination plus the number of
                  shares of Common Stock which the aggregate of the offering
                  price of the total number of shares of Common Stock so offered
                  for subscription or purchase would purchase at such Current

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                  Market Price of the Common Stock and the denominator shall be
                  the number of shares of common Stock outstanding at the close
                  of business on the date fixed for such determination plus the
                  number of shares of Common Stock so offered for subscription
                  or purchase, such reduction to become effective immediately
                  after the opening of business on the day following the date
                  fixed for such determination. For purposes of determining
                  under this paragraph the number of shares of Common Stock
                  outstanding at any time, there shall be excluded all shares of
                  Common Stock held in the treasury of the Company. If any or
                  all such rights or warrants are not so issued or expire or
                  terminate before being exercised, the conversion price then in
                  effect shall be appropriately readjusted.

                           (iii) In case the Company shall distribute to all
                  holders of its Common Stock evidences of its indebtedness or
                  assets (including securities, but excluding cash dividends or
                  a distribution referred to in paragraph (i) above or paid out
                  of surplus) or subscription rights or warrants (excluding
                  those referred to in paragraph (ii) above), the conversion
                  price shall be adjusted so that it shall equal the price
                  determined by multiplying the conversion price in effect
                  immediately prior to the close of business on the date fixed
                  for the determination of stockholders entitled to receive such
                  distribution by a fraction of which the numerator shall be the
                  Current Market Price per share of the Common Stock on the date
                  fixed for such determination less the then fair market value
                  (as determined by the Board of Directors of the Company, in
                  good faith and in the exercise of its reasonable business
                  judgment and described in a Board Resolution filed with any
                  transfer agent for this Series) of the portion of the assets
                  or evidences of indebtedness so distributed applicable to one
                  share of Common Stock and the denominator shall be such
                  Current Market Price per share of the Common Stock. Such
                  adjustment shall become effective immediately prior to the
                  opening of business on the day following the date fixed for
                  the determination of stockholders entitled to receive such
                  distribution.

                           (iv) For the purpose of any computation under
                  paragraphs (ii) and (iii) above, the "Current Market Price"
                  per share of Common Stock on any date shall be deemed to be
                  the

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                  average of the daily closing prices per share of Common Stock
                  for 15 consecutive business days selected by the Company
                  commencing no more than 45 business days before such date. The
                  closing price for each day shall be the last reported sales
                  price regular way or, in case no such sale takes place on such
                  day, the average of the closing bid and asked prices regular
                  way, in either case on the Nasdaq National Market System or,
                  if the Common Stock is not listed or admitted to trading on
                  such Nasdaq National Market System on the principal national
                  securities exchange on which the Common Stock is listed or
                  admitted to trading, or if it is not listed or admitted to
                  trading on any national securities exchange or no such
                  quotations are available, the average of the closing bid and
                  asked prices as furnished by any member of the National
                  Association of Securities Dealers, Inc. selected from time to
                  time by the Company for that purpose, or if no such quotations
                  are available, the fair market value as determined in good
                  faith in the exercise of their reasonable business judgment by
                  the Board of Directors of the Company.

                           (v) All calculations under this Section 1.3(c) shall
                  be made to the nearest cent or to the nearest one-hundredth of
                  a share, as the case may be.

                           (vi) No adjustment in the conversion price shall be
                  required unless such adjustment would require a change of at
                  least 1% in such price; provided, however, that any
                  adjustments which by reason of this paragraph (vi) are not
                  required to be made shall be carried forward and taken into
                  account in any subsequent adjustment.

                  (d) Whenever the conversion price is adjusted as herein
             provided:

                           (i) the Company shall promptly file with any of the
                  transfer agents for this Series a certificate of the principal
                  financial officer of the Company setting forth the adjusted
                  conversion price and showing in reasonable detail the facts
                  upon which such adjustment is based, including a statement of
                  the consideration received or to be received by the Company
                  for any shares of Common Stock issued or deemed to have been
                  issued; and

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                           (ii) a notice stating that the conversion price has
                  been adjusted and setting forth the adjusted conversion price
                  shall forthwith be required, and as soon as practicable after
                  it is required, such notice shall be mailed by the Company to
                  the holders of record of this Series.

                  (e)

                           (i) In case of any consolidation or merger of the
                  Company with or into any other person (other than a merger
                  which does not result in any reclassification, conversion,
                  exchange or cancellation of the Common Stock), or in case of
                  any sale or transfer of all or substantially all of the assets
                  of the Company, or the reclassification of the Common Stock
                  into another form of capital stock of the Company, whether in
                  whole or in part, the holder of each share of this Series
                  shall have the right to receive the kind and amount of
                  securities, cash or property, or any combination thereof which
                  such holder would have been entitled to receive upon such
                  consolidation, merger, sale or transfer or reclassification if
                  he had held the Common Stock issuable upon the conversion of
                  such share of this Series immediately prior to such
                  consolidation, merger, sale or transfer, or reclassification.

                           (ii) In the event that at any time, as a result of
                  paragraph (i) above, the holder of any share of this Series
                  shall become entitled to receive any shares of stock and other
                  securities and property (including, if applicable, Common
                  Stock), thereafter the amount of such shares of stock and
                  other securities so receivable upon conversion of any share of
                  this Series shall be subject to adjustment from time to time
                  in a manner and on terms as nearly equivalent as practicable
                  to the provisions with respect to the Common Stock contained
                  in paragraphs (i) to (vi), inclusive, of section 1.3(c) above,
                  and the provisions of section 1.3(c) with respect to the
                  Common Stock shall apply on like terms to any such shares of
                  stock and other securities and property (including, if
                  applicable, Common Stock).

                  (f) In case:

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                           (i) the Company shall authorize the distribution to
                  all holders of its Common Stock of evidences of its
                  indebtedness or assets (other than cash dividends or other
                  cash distributions paid out of surplus); or

                           (ii) the Company shall authorize the granting to the
                  holders of its Common Stock of rights or warrants to subscribe
                  for or purchase any shares of capital stock of any class or of
                  any other rights; or

                           (iii) of any reclassification of the capital stock of
                  the Company (other than a subdivision or combination of its
                  outstanding shares of Common Stock), or of any consolidation
                  or merger, or of the sale or transfer of all or substantially
                  all of the assets of the Company; or

                           (iv) of the voluntary or involuntary dissolution,
                  liquidation or winding up of the Company;

         then, in each case, the Company shall cause to be filed with any of the
         transfer agents for this Series, and shall cause to be mailed, first
         class postage prepaid, to the holders of record of the outstanding
         shares of this Series, at least 20 days prior to the applicable record
         date hereinafter specified, a notice stating (x) the date on which a
         record is to be taken for the purpose of such dividend, distribution,
         rights or warrants, or, if a record is not to be taken, the date as of
         which the holders of Common Stock of record to be entitled to such
         dividend, distribution, rights or warrants are to be determined, or (y)
         the date on which such reclassification, consolidation, merger, sale,
         transfer, dissolution, liquidation or winding up is expected to become
         effective, and the date as of which it is expected that holders of
         Common Stock of record shall be entitled to exchange their Common Stock
         for securities or other property deliverable upon such
         reclassification, consolidation, merger, sale, transfer, dissolution,
         liquidation or winding up.

                  (g) The Company shall at all times reserve and keep available,
         free from preemptive rights, out of its authorized but unissued Common
         Stock, solely for the purpose of effecting the conversion of the shares
         of this Series, the full number of shares of Common Stock then issuable
         upon the conversion of all outstanding shares of this Series. For the
         purpose of this section 1.3(g), the full number of shares of Common
         Stock issuable upon the conversion of all outstanding shares of this
         Series shall be computed as

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          if at the time of computation of such number of shares of Common Stock
          all outstanding shares of this Series were held by a single holder.
          The Company shall use all reasonable efforts from time to time, in
          accordance with the laws of the State of Delaware, to cause its
          stockholders to increase the authorized amount of its Common Stock if
          at any time the authorized amount of its Common Stock remaining
          unissued shall not be sufficient to permit the conversion of all
          shares of this Series at the time outstanding.

                  (h) The Company will pay any and all taxes that may be payable
         in respect of the issue or delivery of shares of Common Stock on
         conversion of shares of this Series pursuant hereto. The Company shall
         not, however, be required to pay any tax which may be payable in
         respect of any transfer involved in the issue or transfer and delivery
         of shares of Common Stock in a name other than that in which the shares
         of this Series so converted were registered, and no such issue or
         delivery shall be made unless and until the person requesting such
         issue has paid to the Company the amount of any such tax or has
         established to the satisfaction of the Company that such tax has been
         paid.

                  (i) Whenever reference is made in this section 1.3 to the
         issue or sale of shares of Common Stock, the term "Common Stock" shall
         include only shares of the class designated as Common Stock, $.01 par
         value, of the Company at the date hereof or shares of any class or
         classes resulting from any reclassification or reclassifications
         thereof and which have no preference in respect of dividends or of
         amounts payable in the event of any voluntary or involuntary
         liquidation, dissolution or winding up of the Company and which are not
         subject to redemption by the Company, provided that if at any time
         there shall be more than one such resulting class, the shares of each
         such class then so deliverable shall be substantially in the proportion
         which the total number of shares of such class resulting from all such
         reclassifications bears to the total number of shares of all such
         classes resulting from all such reclassifications.

                  (j) Upon any conversion of shares of this Series, the shares
         so converted shall have the status of authorized and unissued shares of
         preferred stock, unclassified as to series, and the number of shares of
         preferred stock which the Company shall have authority to issue shall
         not be decreased by the conversion of shares of this Series.

         1.4 Liquidation Rights. In the event of any liquidation, dissolution,
or winding up of the affairs of the Company, whether voluntary or otherwise,
after payment or provision for payment of the debts and other liabilities of the

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Company, the holders of this Series shall be entitled to receive an amount in
cash for each share of this Series equal to $10.00 per share, plus an amount
equal to all dividends accumulated and unpaid on each such share up to the date
fixed for distribution, before any distributions shall be made to the holders of
the Common Stock and of any other capital stock of the Company ranking junior to
this Series upon the liquidation, dissolution or winding up of the Company. If
upon any liquidation, dissolution or winding up of the Company, the assets
distributable among the holders of this Series shall be insufficient to permit
the payment in full to the holders of all the then outstanding shares of this
Series and all holders of preferred stock ranking on a parity with this Series
with respect to the payment upon liquidation, dissolution and winding up of the
Company of all preferential amounts payable to all such holders, then the entire
assets of the Company thus distributable shall be distributed ratably among the
holders of this Series and all such other holders of Preferred Stock in
proportion to the respective amounts that would be payable per share if such
assets were sufficient to permit payment in full. Subject to the provisions of
section 1.3(e)(i), a consolidation or merger of the Company with or into one or
more persons or the sale or transfer of all or substantially all of the assets
of the Company shall not be deemed to be a liquidation, dissolution or winding
up of the Company.

         1.5 Optional Cash Redemption. The shares of this Series are not
redeemable prior to October 20, 1999. Thereafter, the shares of this Series are
redeemable for cash, in whole at any time or from time to time in part at the
option of the Company, at a redemption price of $10.00 per share, plus any
accumulated and unpaid dividends thereon.

         Notice of redemption pursuant to this Section 1.5 will be mailed at
least 30 days but not more than 60 days before the redemption date to each
holder of record of shares of this Series to be redeemed at the address shown on
the stock books of the Company (but no failure to mail such notice or any defect
therein or in the mailing thereof shall affect the validity of the proceedings
for such redemption except as to the holder to whom the Company has failed to
mail such notice or except as to the holder whose notice was defective). On and
after the redemption date, dividends shall cease to accumulate on shares of this
Series called for redemption (unless the Company defaults in the payment of the
redemption price).

         If less than all the outstanding shares of this Series not previously
called for redemption are to be redeemed pursuant to this Section 1.5, shares to
be redeemed shall be selected by the Company from outstanding shares not
previously called for redemption by lot or pro rata (as nearly as may be) as
determined by the Board of Directors of the Company. The Company may not

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redeem less than all outstanding shares of this Series pursuant to this Section
1.5 unless full cumulative dividends shall have been declared and paid or set
apart for payment upon all outstanding shares of this Series for all past
dividend periods. Shares of this Series redeemed by the Company shall, after
such redemption, have the status of authorized but unissued shares of preferred
stock, without designation as to series, and may thereafter be issued.

         1.6 Voting Rights. The holders of shares of this Series shall have no
right to vote for any purpose, except as specifically required by the laws of
the State of Delaware and except as follows:

                  So long as any shares of this Series remain outstanding, the
         affirmative vote or consent of the holders of a majority of the then
         outstanding shares of this Series, in person or by proxy, either in
         writing or at a meeting called for that purpose (voting as a class with
         the holders of all other series of preferred stock ranking on a parity
         with this Series either as to dividends or distributions or upon
         liquidation, dissolution or winding up of the Company and upon which
         like voting rights have been conferred and are then exercisable), shall
         be necessary to permit, effect or validate the repeal, amendment or
         other change of any provision of the Certificate of Incorporation of
         the Company in any manner which materially and adversely affects the
         rights, preferences, or privileges of this Series or the holders
         thereof; provided, however, that any increase or decrease (but not
         below the number of shares of this Series then outstanding) in the
         amount of authorized preferred stock or the creation and issuance of
         other series of preferred stock, whether ranking on a parity with or
         junior or prior to this Series with respect to voting, the payment of
         dividends or the distribution of assets upon liquidation, dissolution
         or winding up shall not be deemed to materially and adversely affect
         such rights, preferences or privileges. In connection with any right to
         vote, each holder of outstanding shares of this Series shall have one
         vote for each share held.

         The foregoing voting provisions will not apply if, at or prior to the
time when the act with respect to which such vote would otherwise be required
shall be effected, all outstanding shares of this Series shall have been
redeemed or sufficient funds shall have been deposited in trust to effect such
redemption.


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         IN WITNESS WHEREOF, this Certificate has been executed and attested by
the undersigned on October 19, 1998, and shall be effective at 10:00 a.m.
Eastern Daylight Time on the date on which filed with the Secretary of State of
the State of Delaware.


                                     PARALLEL PETROLEUM CORPORATION



                                     By: /s/ Larry C. Oldham
                                         -----------------------------
                                         Larry C. Oldham, President

ATTEST:


 /s/ Thomas W. Ortloff
----------------------------
Thomas W. Ortloff, Secretary


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