<PAGE>
 
                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549


                                   FORM 10-Q


[X]   QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
      SECURITIES EXCHANGE ACT OF 1934

      FOR THE QUARTERLY PERIOD ENDED MARCH 31, 1998


[ ]   TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
      SECURITIES EXCHANGE ACT OF 1934

      For the transition period from ____________ to ____________

                         Commission file number: 0-9808

                             PLAINS RESOURCES INC.
             (Exact name of registrant as specified in its charter)


          DELAWARE                                     13-2898764
(State or other jurisdiction of                     (I.R.S. Employer
incorporation or organization)                     Identification No.)



                               500 DALLAS STREET
                              HOUSTON, TEXAS 77002
                    (Address of principal executive offices)
                                   (Zip Code)

                                 (713) 654-1414
              (Registrant's telephone number, including area code)

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.   YES    X     NO 
                                          -----      ----- 

16,833,431 shares of common stock $.10 par value, issued and outstanding at May
11, 1998.

                                  Page 1 of 15
<PAGE>
 
                     PLAINS RESOURCES INC. AND SUBSIDIARIES
                               TABLE OF CONTENTS

<TABLE> 
<CAPTION> 
                                                                            PAGE
<S>                                                                         <C> 
PART I.  FINANCIAL INFORMATION

CONSOLIDATED FINANCIAL STATEMENTS:
 
   Consolidated Balance Sheets:
     March 31, 1998 and December 31, 1997.................                    3
   Consolidated Statements of Income:                                        
     For the three months ended March 31, 1998 and 1997...                    4
   Consolidated Statements of Cash Flows:                                    
     For the three months ended March 31, 1998 and 1997...                    5
   Notes to Consolidated Financial Statements.............                    6
                                                                             
MANAGEMENT'S DISCUSSION AND ANALYSIS......................                    8
                                                                             
PART II.  OTHER INFORMATION...............................                   14
 
</TABLE>

                                  Page 2 of 15
<PAGE>
 
PLAINS RESOURCES INC. AND SUBSIDIARIES
CONSOLIDATED BALANCE SHEETS (IN THOUSANDS, EXCEPT SHARE DATA)
--------------------------------------------------------------------------------

                                              MARCH 31,         DECEMBER 31,
                                                1998                1997
                                              ----------        ------------
                                              (UNAUDITED) 

                   ASSETS
CURRENT ASSETS
Cash and cash equivalents                     $  29,906          $   3,714
Accounts receivable                              71,502             99,597
Inventory                                        22,418             22,802
Prepaids and other                                  905                667
                                              ---------          ---------
Total current assets                            124,731            126,780
                                              ---------          ---------
PROPERTY AND EQUIPMENT
Oil and natural gas properties - full cost
 method:
  Subject to amortization                       515,610            498,038
  Not subject to amortization                    53,394             52,024
Midstream assets, primarily crude oil
 terminal and storage facility                   35,510             35,451
Other property and equipment                      8,321              8,074
                                              ---------          ---------
                                                612,835            593,587
Less allowance for depreciation, depletion
 and amortization                              (186,711)          (180,279)
                                              ---------          ---------
                                                426,124            413,308
                                              ---------          ---------
                                                 16,378             16,731
                                              ---------          ---------
OTHER ASSETS                                  $ 567,233          $ 556,819
                                              =========          =========

                   LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT LIABILITIES
Accounts payable and other current 
 liabilities                                  $  87,236          $ 102,663
Interest payable                                  1,600              6,601
Royalties payable                                 4,908              5,016
Notes payable and other current obligations       1,261             18,511
                                              ---------          ---------
Total current liabilities                        95,005            132,791

BANK DEBT                                       126,560             80,000
SUBORDINATED DEBT                               202,605            202,661
OTHER LONG-TERM DEBT                              3,067              3,067
OTHER LONG-TERM LIABILITIES                       5,089              5,107
                                              ---------          ---------
                                                432,326            423,626
                                              ---------          ---------
STOCKHOLDERS' EQUITY
Series D Cumulative Convertible Preferred
 Stock, $1.00 par value, 46,600 shares
 authorized, issued and outstanding, net
 of discount of $2,317,000 and $2,629,000
 at March 31, 1998 and December 31, 1997,
 respectively                                    20,983             20,671
Common stock, $.10 par value, 50,000,000
 shares authorized; issued and outstanding
 16,745,207 at March 31, 1998, and
 16,703,074 shares at December 31, 1997           1,675              1,670
Additional paid-in capital                      123,165            122,887 
Accumulated deficit                             (10,916)           (12,035)
                                              ---------          ---------
                                                134,907            133,193
                                              ---------          ---------
                                              $ 567,233          $ 556,819
                                              =========          =========

                See notes to consolidated financial statements.

                                  Page 3 of 15
<PAGE>
 
PLAINS RESOURCES INC. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF INCOME (UNAUDITED) (IN THOUSANDS, EXCEPT PER SHARE
 DATA)
--------------------------------------------------------------------------------

                                                 THREE MONTHS ENDED
                                                      MARCH 31,
                                                 ------------------
                                                  1998        1997
                                                 ------      ------

REVENUE
Oil and natural gas sales                        $ 26,164    $ 26,279
Marketing, transportation and storage             167,204     180,795
Interest and other income                             204          58
                                                 --------    --------
                                                  193,572     207,132
                                                 --------    --------
EXPENSES
Production expenses                                12,838      10,194
Purchases, transportation and storage             163,200     178,329
General and administrative                          2,376       2,095
Depreciation, depletion and amortization            6,755       5,320
Interest expense                                    6,109       4,710
                                                 --------    --------
                                                  191,278     200,648
                                                 --------    --------
Income before income taxes                          2,294       6,484
Income tax expense:
  Current                                               3         114
  Deferred                                            860       2,479
                                                 --------    --------
NET INCOME                                       $  1,431    $  3,891
                                                 ========    ========
Less: cumulative preferred stock dividends            312          --
                                                 --------    --------
NET INCOME AVAILABLE TO COMMON STOCKHOLDERS      $  1,119    $  3,891
                                                 ========    ========
Earnings per share:
  Basic                                          $   0.07    $   0.24
                                                 ========    ========
  Diluted                                        $   0.06    $   0.22
                                                 ========    ========

          See notes to consolidated financial statements.

                                  Page 4 of 15
<PAGE>
 
PLAINS RESOURCES INC. AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CASH FLOWS (UNAUDITED) (IN THOUSANDS)
--------------------------------------------------------------------------------

                                                 THREE MONTHS ENDED
                                                      MARCH 31,
                                                 ------------------
                                                  1998        1997
                                                 ------      ------

CASH FLOWS FROM OPERATING ACTIVITIES
Net income                                       $  1,431    $  3,891
Items not affecting cash flows from operating
 activities:
  Depreciation, depletion and amortization          6,755       5,320
  Deferred income taxes                               860       2,479
  Other noncash items                                  54          85
Change in assets and liabilities resulting
 from operating activities:
  Accounts receivable                              27,749       6,618
  Inventory                                           384      (5,647)
  Prepaids and other                                 (228)        248
  Accounts payable and other current 
   liabilities                                    (18,881)     (3,528)
  Interest payable                                 (4,308)     (3,019)
  Royalties payable                                    13         581
                                                 --------    --------        
Net cash provided by operating activities          13,829       7,028
                                                 --------    --------
CASH FLOWS FROM INVESTING ACTIVITIES
Payment for acquisition, exploration and 
 development costs                                (15,944)    (35,481)
Payment for additions to other property 
 and assets                                          (315)     (4,158)
                                                 --------    --------
Net cash used in investing activities             (16,259)    (39,639)
                                                 --------    --------
CASH FLOWS FROM FINANCING ACTIVITIES
Proceeds from long-term debt                       75,560      68,300
Proceeds from short-term debt                         750          --
Principal payments of long-term debt              (29,000)    (37,000)
Principal payments of short-term debt             (18,000)         --
Other                                                (688)        (92)
                                                 --------    -------- 
Net cash provided by financing activities          28,622      31,208
                                                 --------    --------
Net increase (decrease) in cash and cash
 equivalents                                       26,192      (1,403)
Cash and cash equivalents, beginning of period      3,714       2,517
                                                 --------    --------
Cash and cash equivalents, end of period         $ 29,906    $  1,114
                                                 ========    ========

                See notes to consolidated financial statements.

                                  Page 5 of 15
<PAGE>
 
                     PLAINS RESOURCES INC. AND SUBSIDIARIES

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                        
                                 March 31, 1998
                                  (UNAUDITED)

Note 1 -- Accounting Policies


The accompanying unaudited consolidated financial statements have been prepared
in accordance with the instructions to interim financial reporting as prescribed
by the Securities and Exchange Commission ("SEC"). For further information,
refer to the consolidated financial statements and notes thereto included in the
Company's Annual Report on Form 10-K for the year ended December 31, 1997, filed
with the SEC.


All material adjustments consisting only of normal recurring adjustments which,
in the opinion of management, were necessary for a fair statement of the results
for the interim periods, have been reflected.  Certain reclassifications have
been made to the prior year statements to conform with the current year
presentation. The Company evaluates the capitalized costs of its oil and natural
gas properties on an ongoing basis and has utilized the most recently available
information to estimate its reserves at March 31, 1998, in order to determine
the realizability of such capitalized costs.  Future events, including drilling
activities, product prices and operating costs, may affect future estimates of
such reserves.


NOTE 2 -- ACQUISITION

On March 21, 1998, Plains All American Inc., a wholly owned unrestricted
subsidiary of the Company, as defined in the indenture for the Company's $200
million 10.25% Senior Subordinated Notes (the "Indenture"), entered into a
definitive agreement to acquire all of the outstanding capital stock of the All
American Pipeline Company, Celeron Gathering Corporation and Celeron Trading &
Transportation Company (collectively the "Celeron Companies") from The Goodyear
Tire & Rubber Company ("Goodyear"). The agreement provides for a purchase price
of $396 million and for dividends to be paid by the Celeron Companies to
Goodyear between January 1, 1998, and closing in an amount not to exceed $25.1
million, resulting in aggregate proceeds to Goodyear of approximately $420
million. Net of the dividends to be paid to Goodyear, the Company estimates the
aggregate amount payable at closing, inclusive of estimated closing costs and
net of working capital to be acquired will approximate $400 million. The
principal assets of the entities to be acquired include the All American
Pipeline System, a 1,233-mile crude oil pipeline extending from California to
Texas, and a 45-mile crude oil gathering system in the San Joaquin Valley of
California, as well as other assets related to such operations. The purchase
price is subject to certain adjustments through the closing date, and the
transaction is subject to regulatory review and approval. The transaction is
expected to be completed in the third quarter of 1998 after regulatory approvals
by the United States Department of Justice and the Federal Trade Commission
under the Hart-Scott-Rodino Anti-Trust Improvements Act of 1976, as amended, and
by the Public Utilities Commission of the State of California have been secured.

                                  Page 6 of 15
<PAGE>
 
NOTE 3 -- EARNINGS PER SHARE

The following is a reconciliation of the numerators and the denominators of the
basic and diluted earnings per share ("EPS") computations for income from
continuing operations for the three months ended March 31, 1998 and 1997, as
required by Statement of Financial Accounting Standards No. 128 ("SFAS 128"),
Earnings Per Share.  Prior period EPS data has been restated in accordance with
the provisions of SFAS 128.

<TABLE>
<CAPTION>
                                                                          For the Quarter ended March 31,
                                      --------------------------------------------------------------------------------------------- 

                                                              1998                                               1997
                                      ----------------------------------------------------------------------------------------------

                                            Income             SHARES            PER           INCOME             SHARES       PER
                                           (NUMERA            (DENOMI           SHARE          (NUMERA           (DENOMI      SHARE
                                            -TOR)              -NATOR)          AMOUNT          -TOR              -NATOR)     AMOUNT

                                      ----------------------------------------------------------------------------------------------

                                                                       (in thousands, except per share data)
                                                                                    (UNAUDITED)
<S>                                      <C>                   <C>              <C>              <C>              <C>         <C>
Net income                                 $   1,431                                        $   3,891
Less:  preferred stock dividends                (312)                                              --
                                           ---------                                        ---------
Income available to common                     
     stockholders                              1,119           16,724        $  0.07            3,891             16,535     $ 0.24 
                                                                             =======                                         ======
Effect of dilutive securities:                                 
     Employee stock options                       --            1,029                              --              1,003
     Warrants                                     --              518                              --                493
                                           ---------           ------                       ---------             ------
Income available to common                 
     stockholders assuming dilution        $   1,119           18,271        $  0.06        $   3,891             18,031     $ 0.22 
                                           =========           ======        =======        =========             ======     ======
</TABLE>

                                  Page 7 of 15
<PAGE>
 
                      MANAGEMENT'S DISCUSSION AND ANALYSIS


RESULTS OF OPERATIONS

Three month periods ended March 31, 1998 and 1997

The Company reported increases in the fundamental performance drivers in both
its operating segments during the first quarter of 1998.  Oil and gas production
in the upstream segment increased 19% and gross margin from midstream activities
increased 62% over the similar results from last year's first quarter.  Despite
the significant improvement in controllable aspects of the Company's operations,
financial results were adversely affected by a 30% decline in the average
benchmark oil price between the two periods. The NYMEX benchmark oil price
averaged $15.97 per barrel in the first quarter of 1998, compared to the $22.83
per barrel average for the first quarter of 1997.

For the quarter ended March 31, 1998, the Company reported net income of $1.4
million, or $.07 per share ($.06 per share assuming dilution).  This compares
with net income in the prior year period of $3.9 million or $.24 per share ($.22
per share assuming dilution) on substantially higher oil prices. Earnings before
interest, taxes, depreciation and amortization ("EBITDA") for the first quarter
of 1998 totaled $15.3 million, a 7% decline from the $16.5 million reported for
the prior year period.  Cash flow from operations (net income plus noncash
expenses) was $9.1 million for the first quarter of 1998 as compared to $11.8
million in last year's first quarter.  Net cash provided by operating
activities, as reported in the consolidated statements of cash flows, increased
to $13.8 million for the three months ended March 31, 1998, as compared to $7.0
million for the 1997 comparative period. Such increase is primarily due to an 
increase in inventory levels in the prior year period and the timing of cash
receipts and payments between the two periods.

Upstream Results

The following table sets forth certain upstream operating information of the
Company for the periods presented:

 
                                         THREE MONTHS ENDED
                                              MARCH 31,
                                     ------------------------
                                          1998            1997
                                     ------------    ------------
                                           (IN THOUSANDS,
                                        EXCEPT PER UNIT DATA)
                                             (UNAUDITED)
AVERAGE DAILY PRODUCTION VOLUMES
Barrels of oil equivalent ("BOE")
  California (91% oil)                   13.7              10.1
  S. Florida (100% oil)                   4.9               5.2
  Illinois Basin (100% oil)               3.7               3.4
  Sold Properties                          --               0.1
                                        -----             -----
  Total (94% oil)                        22.3              18.8
                                        =====             =====
UNIT ECONOMICS
  Average sales price per BOE          $13.03            $15.51
  Production expenses per BOE            6.39              6.02
                                        -----             -----
  Gross margin per BOE                   6.64              9.49
  Upstream G&A expense per BOE           0.69              0.74
                                       ------            ------
  Gross profit per BOE                 $ 5.95            $ 8.75
                                       ======            ======


Oil and natural gas production for the first quarter of 1998 increased
approximately 19% to an average of 22,300 BOE per day as compared to the first
quarter 1997 average of 18,800 BOE per day. The increase in production volumes 
is primarily attributable to the Company's ongoing exploitation activities on 
its three core properties and to the acquisition of two California producing
properties during 1997. The

                                  Page 8 of 15
<PAGE>
 
Montebello and the Arroyo Grande Fields were acquired during the first quarter 
and fourth quarter of 1997, respectively. Excluding the impact of these 
acquisitions, total production was up approximately 8% from the prior year 
quarter.

Net daily production in California increased approximately 36% to 13,700 BOE in
the first quarter of 1998 compared to 10,100 BOE in the same quarter of 1997.
Excluding production from the two 1997 acquisitions, total California production
was up approximately 15% over the comparative prior year quarter.  During the
first quarter of 1998, the Company's California properties experienced
production downtime of approximately 15,000 barrels due to El Nino related
weather conditions.  Net daily production in the Illinois Basin averaged
approximately 3,700 barrels per day during the first quarter of 1998, an
increase of approximately 9% as compared to the 1997 first quarter average of
3,400 barrels per day.  Net daily production in South Florida averaged
approximately 4,900 barrels per day during the first quarter of 1998, a 6%
decrease from the 1997 comparative period.  Barge logistic problems and, to a
lesser extent, workover activity had a negative impact of approximately 29,000
net barrels in South Florida during the first quarter of 1998. Due to the high
volume of production that is generated by a few wells in South Florida, abrupt
or abnormal declines or downtime due to mechanical, marketing, or other
conditions on any of the properties in this area could have a significant impact
on production.

Oil and natural gas revenues remained constant at $26.2 million for the first
quarter of 1998 as decreased product prices offset increased production volumes.
The Company's average product price, which represents a combination of fixed and
floating price sales arrangements and incorporates location and quality
discounts from the benchmark NYMEX price was $13.03 per BOE, a decrease of
approximately 16% as compared to 1997's first quarter average wellhead price of
$15.51 per BOE.  The NYMEX benchmark West Texas Intermediate ("WTI") crude oil
price averaged $15.97 per barrel during the 1998 first quarter, 30% or $6.86 per
barrel below the $22.83 per barrel average for the first quarter of 1997.  The
Company maintained hedges on approximately 60% and 80% of its crude oil
production in the first quarter of 1998 and 1997, respectively, with the current
year's hedge price averaging a NYMEX WTI price of approximately $19.80 per
barrel, approximately $.80 per barrel higher than last year's average hedge
price. Hedging transactions had the effect of increasing the Company's average
price per BOE by $2.10 in the first quarter of 1998 and decreasing such price by
approximately $3.58 per BOE in the 1997 first quarter.

The Company was also negatively affected by higher location and quality
differentials from the NYMEX benchmark price, particularly in South Florida,
where the differential was approximately $9.00 per barrel in the current year
quarter, approximately $2 per barrel higher than the prior year quarter.  The
Company's weighted average differential for all areas was approximately $5.10
per barrel for the 1998 first quarter, compared to approximately $3.75 per
barrel during last year's first quarter.


Unit gross margin in the upstream segment was $6.64 per BOE, a 30% decrease as
compared to $9.49 per BOE reported for the first quarter of 1997 on
substantially higher oil prices.  Upstream unit gross profit, which deducts all
pre-interest cash costs, was $5.95 per BOE, 32% lower than the 1997 amount of
$8.75 per BOE.  Unit production expenses increased by 6% to $6.39 per BOE for
the first quarter of 1998, from $6.02 for the prior year quarter.  El Nino
related expenses in California accounted for approximately $.20 per BOE or 54%
of the increase. Total production expenses increased to $12.8 million from $10.2
million for the first quarter of 1997 primarily due to increased production
volumes related to the Company's acquisition and exploitation activities and to
the El Nino related expenses.

                                  Page 9 of 15
<PAGE>
 
Unit general and administrative ("G&A") expense in the upstream segment declined
7% to $.69 per BOE from $.74 per BOE primarily due to increased production
levels.  Depreciation, depletion and amortization ("DD&A") per BOE was $3.00 for
the first quarter of 1998 compared to $2.75 per BOE in the 1997 comparative
quarter.  Such increase is primarily attributable to the impact of lower
commodity prices on proved reserve volumes.  Total DD&A expense increased to
$6.8 million from $5.3 million due to increased production volumes.


Midstream Results

The following table sets forth certain midstream operating information of the
Company for the periods presented:

 
                                               THREE MONTHS
                                                   ENDED
                                                 MARCH 31,
                                           ------------------
                                            1998        1997
                                           ------     -------
                                              (IN THOUSANDS)
                                                (UNAUDITED)

OPERATING RESULTS
     Gross Margin                          $4,004     $2,466
     G&A expense                              986        837
                                           ------     ------
     Gross profit                          $3,018     $1,629
                                           ======     ====== 

AVERAGE DAILY VOLUMES
     Crude oil barrels marketed                81         63
     Crude oil terminal throughput barrels     55         71  

The Company's midstream segment reported gross margin (marketing, transportation
and storage revenues less purchases, transportation and storage expenses) of
$4.0 million for the first quarter of 1998, reflecting an approximate 62%
increase over the $2.5 million reported for the 1997 quarter. Gross profit
(gross margin less midstream G&A expenses) increased 85% to $3.0 million versus
$1.6 million in the first quarter of 1997.  Net of interest expense associated
with contango inventory transactions, midstream gross margin and gross profit
for the current year quarter were $3.9 million and $2.9 million, respectively,
representing increases of approximately 56% and 76% over the 1997 respective
amounts. The Company did not have any contango inventory transactions in the
prior year quarter. The increases in gross margin and gross profit are due to
increased marketing activities, strong marketing margins in areas where the
Company conducts a large part of its marketing activities which offset weaker
marketing margins in other areas and to profits from contango crude oil
inventory transactions.  Gross revenues decreased to $167.2 million from $180.8
million for the prior year quarter due to the decrease in crude oil prices
between the two periods. Midstream G&A expenses increased from $837,000 to
$986,000 in the current year quarter primarily as a result of additional
personnel added to further expand marketing activities.  Average crude oil
volumes marketed increased approximately 29% to 81,000 barrels per day from
63,000 barrels per day averaged during the 1997 quarter.  Because the crude oil
market was in contango during the first quarter of 1998, the Company utilized
its storage and terminal facility in Cushing, Oklahoma (the "Cushing Terminal")
to take advantage of available market arbitrages. Accordingly, average volumes
terminalled through the Cushing Terminal decreased about 16,000 barrels per day
to 55,000 barrels in the 1998 first quarter from 71,000 barrels per day in the
1997 comparative period.

                                 Page 10 of 15
<PAGE>
 
General

Total G&A expense increased approximately 13% to $2.4 million for the first
quarter of 1998.  The increase is a result of higher G&A expenses in the
midstream segment primarily due to expansion of the Company's marketing
activities and to increased expenses in the upstream segment primarily related
to the Company's 1997 acquisitions.  Unit upstream G&A expense declined 7% to
$.69 per BOE in the first quarter of 1998 due to increased production volumes.



Interest expense for the quarter ended March 31, 1998, increased to $6.1 million
from $4.7 million for the comparative prior year quarter primarily due to higher
outstanding debt which was partially offset by a slightly lower overall average
interest rate.  The current year quarter includes approximately $.2 million of
interest associated with amounts borrowed to fund the Company's capital
contribution to Plains All American Inc. ("Plains All American"). See "Capital
Resources, Liquidity and Financial Condition".  Capitalized interest was $.9
million and $.7 million for the three months ended March 31, 1998 and 1997,
respectively.

The Company's total tax provision for the quarter ended March 31, 1998, was
approximately $.9 million, as compared to the first quarter 1997 tax provision
of approximately $2.6 million.  Such decrease is due to the decrease in income
before taxes between the two periods and a slight decrease in the Company's
effective tax rate.  In both periods, substantially all of the Company's income
tax provision was deferred.

In July 1997, the FASB issued Statement of Financial Accounting Standards No.
131 ("SFAS 131"), Disclosures About Segments of an Enterprise and Related
Information, effective for fiscal years beginning after December 15, 1997.  SFAS
131 introduces a new model for segment reporting and requires disclosures for
each segment that are similar to those required under current standards with the
addition of quarterly disclosure requirements and a finer partitioning of
geographic disclosures.  Reportable segments are based on products and services,
geography, legal structure, management structure or any manner in which
management disaggregates a company.  This statement replaces the notion of
industry and geographic segments in current FASB standards.  Management is
currently evaluating the impact of this statement on the Company's disclosures.


CAPITAL RESOURCES, LIQUIDITY AND FINANCIAL CONDITION

On March 21, 1998, Plains All American, a wholly owned unrestricted subsidiary
of the Company, as defined in the indenture ("Indenture") for the Company's $200
million 10.25% Senior Subordinated Notes (the "10.25% Notes"), entered into a
definitive agreement to acquire all of the outstanding capital stock of the All
American Pipeline Company, Celeron Gathering Corporation and Celeron Trading &
Transportation Company (collectively the "Celeron Companies") from The Goodyear
Tire & Rubber Company ("Goodyear") The agreement provides for a purchase price
of $396 million and for dividends to be paid by the Celeron Companies to
Goodyear between January 1, 1998, and closing in an amount not to exceed $25.1
million, resulting in aggregate proceeds to Goodyear of approximately $420
million. Net of the dividends to be paid to Goodyear, the Company estimates the
aggregate amount payable at closing, inclusive of estimated closing costs and
net of working capital to be acquired will approximate $400 million. The
principal assets of the entities to be acquired include the All American
Pipeline System, a 1,233-mile crude oil pipeline extending from California to
Texas, and a 45-mile crude oil gathering system in the San Joaquin Valley of
California, as well as other assets related to such operations. The purchase
price is subject to certain adjustments through the closing date, and the
transaction is subject to regulatory review and approval. The transaction is
expected to be completed in the third quarter of 1998 after regulatory approvals
by the United States Department of Justice and the Federal Trade Commission
under the Hart-Scott-Rodino Anti-Trust Improvements Act 

                                 Page 11 of 15
<PAGE>
 
of 1976, as amended, and by the Public Utilities Commission of the State of
California have been secured.

A major portion of the financing for the transaction will be provided through a
new $325 million, limited recourse bank facility made available to Plains All
American by ING Barings and BankBoston N.A. In addition to the bank facility,
the Company will make a minimum capital contribution to Plains All American of
$110 million which will be used to fund the balance of the purchase price and
transaction costs and provide initial working capital.  To finance its capital
contribution, the Company will borrow a minimum of $25 million under the
Company's Revolving Credit Facility (the "Revolving Credit Facility") and has
entered into financing commitments for a new issue of privately placed,
convertible preferred stock aggregating approximately $85 million. Commitments
for the preferred stock placement have been obtained from a group of equity
investors comprised primarily of existing shareholders. In addition to the
preferred stock, the Company has the flexibility under the covenants of its
Indenture and Revolving Credit Facility to contribute an aggregate of
approximately $55 million to Plains All American.

During the quarter, the Company made a capital contribution of approximately $29
million to Plains All American. The capital contribution was made during the
first quarter due to the uncertainty of crude oil prices and the resulting
potential limitations at a later date from the debt incurrence covenants
contained in the Indenture for the 10.25% Notes. The capital contribution was
made with existing cash on hand and proceeds from the Revolving Credit Facility.
At March 31, 1998, the Company had approximately $126.6 million in borrowings
and a $1.0 million standby letter of credit outstanding under the Revolving
Credit Facility. The Company anticipates increasing the size of the Revolving
Credit Facility by $60 million to a total of $225 million of aggregate borrowing
capacity.

At March 31, 1998, the Company had working capital of approximately $29.7
million including the amount contributed to Plains All American which is
currently invested in short-term investments.  Excluding such contribution, the
Company had working capital of approximately $1.0 million compared to a working
capital deficit of $6.0 million at December 31, 1997. The Company has
historically operated with a working capital deficit due primarily to ongoing
capital expenditures that have been financed through cash flow and the Revolving
Credit Facility.

INVESTING AND FINANCING ACTIVITIES

Net cash flows used in investing activities were $16.3 million and $39.6 million
for the three months ended March 31, 1998 and 1997, respectively.  Investing
activities include payments for acquisition, exploration and development costs
of $15.9 million and $35.5 million for these same periods, respectively.
Included in the 1997 amount is approximately $25 million related to the
acquisition of the Montebello field.

Net cash provided by financing activities amounted to $28.6 million and $31.2
million for the three months ended March 31, 1998 and 1997, respectively.
Approximately $16 million and $25 million borrowed under the Revolving Credit
Facility to fund the capital contribution to Plains All American and the
acquisition of the Montebello field is included in proceeds from long-term debt
in 1998 and 1997, respectively. Included in both years are net proceeds from
borrowings under the Revolving Credit Facility as a result of acquisition,
exploration and development activities. Financing activities during the first
quarter of 1998 include approximately $.8 million in short-term borrowings and
approximately $18 million of repayments related to contango crude oil inventory
transactions at the Cushing Terminal.

                                 Page 12 of 15
<PAGE>
 
CHANGING OIL AND NATURAL GAS PRICES

The Company is affected by changes in crude oil prices, which have historically
been volatile.  Although the Company has routinely hedged a substantial portion
of its crude oil production and intends to continue this practice, prolonged low
crude oil prices or future crude oil price declines would have a negative impact
on the Company's overall results, and therefore its liquidity. Furthermore, low
crude oil prices could affect the Company's ability to raise capital on terms
favorable to the Company. In order to manage its exposure to commodity price
risk, the Company has routinely hedged a portion of its crude oil production.
For 1998, the Company has entered into various fixed price arrangements on
approximately 12,250 barrels of oil per day, or approximately 60% of 1998 first
quarter crude oil production at a NYMEX WTI price of approximately $19.80 per
barrel. In addition, the Company also has fixed price arrangements on 9,000
barrels per day in 1999 at a NYMEX WTI price of $18.25 per barrel, or
approximately 40% of first quarter 1998 crude oil production levels. The
foregoing NYMEX WTI prices are before quality and location differentials.
Management intends to continue to maintain hedging arrangements for a
significant portion of its production. Such contracts may expose the Company to
the risk of financial loss in certain circumstances.

Additionally, decreases in the prices of oil and natural gas have had, and
could have in the future, an adverse effect on the carrying value of the
Company's proved reserves and the Company's revenues, profitability and cash
flow.  Almost all of the Company's reserve base (approximately 94% of year-end
1997 reserve volumes) is comprised of long-life oil properties that are
sensitive to crude oil price volatility.  The crude oil price received by the
Company at December 31, 1997, upon which proved reserve volumes, the estimated
present value (discounted at 10%) of future net revenue from the Company's
proved oil and natural gas reserves (the "Present Value of Proved Reserves") and
the Present Value of Proved Reserves reduced by future discounted income taxes
(the "Standardized Measure") as of such date were based, was $18.34 per barrel.
During 1998, the benchmark NYMEX crude oil price has fluctuated significantly,
closing as high as $17.82 per barrel and as low as $13.21 per barrel. Under full
cost accounting rules as prescribed by the SEC, unamortized costs of proved oil
and natural gas properties are subject to a ceiling, which limits such costs to
the Standardized Measure.  At December 31, 1997, the Standardized Measure of the
Company's proved reserves was greater than the book carrying cost of the
Company's oil and gas properties by approximately $85 million.  Subject to
ongoing exploitation and production activities which may affect the estimated
volumes and values of the Company's oil and gas properties, the Company
estimates that the Standardized Measure of the Company's proved reserves will
approximate the book carrying cost of such properties at a NYMEX benchmark crude
oil price between $15.00 and $16.00 per barrel and in the future the Company
could be required to record a noncash writedown of such capitalized costs. This
estimated price range is based on average historical differentials between the
NYMEX WTI benchmark oil price and the Company's average wellhead realizations.
Such wellhead realizations are affected by quality and location factors.
Variations from these average differentials at any given point in time will
affect the Company's estimates of proved reserve volumes and values.

FORWARD-LOOKING STATEMENTS AND ASSOCIATED RISKS

All statements, other than statements of historical facts, included in this
report which address activities, events or developments that the Company expects
or anticipates will or may occur in the future are forward-looking statements.
Such forward-looking statements are subject to risks and uncertainties
including, among other things, market conditions, drilling and operating
hazards, uncertainties inherent in estimating oil and gas reserves and other
factors discussed in the Company's Annual Report on Form 10-K for the year ended
December 31, 1997.

                                 Page 13 of 15
<PAGE>
 
PART II.  OTHER INFORMATION

Item 1 - Legal Proceedings

  None

Item 2 - Material Modification of Rights of Registrant's Securities

  None

Item 3 - Defaults on Senior Securities

  None

Item 4 - Submission of Matters to a Vote of Security Holders

  None

Item 5 - Other Information

  None

Item 6  Exhibits and Reports on Form 8-K

  A. Exhibits

     27.  Financial Data Schedule

  B. Report on Form 8-K

     A Form 8-K with respect to the News Release announcing the Company's
     agreement for the purchase by Plains All American Inc. (a wholly owned
     subsidiary of the Company) of all outstanding capital stock of the All
     American Pipeline Company, Celeron Gathering Corporation and Celeron
     Trading & Transportation Company from a subsidiary of The Goodyear Tire &
     Rubber Company was filed on March 23, 1998.  Such Form 8-K is hereby
     incorporated by reference.

                                 Page 14 of 15
<PAGE>
 
                                   SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned and thereunto duly authorized.



                               PLAINS RESOURCES INC.



Date: May 15, 1998             By:  /s/  Cynthia A. Feeback              
                                    ----------------------------------------
                                    Cynthia A. Feeback, Controller and
                                    Principal Accounting Officer
                                    (Principal Accounting Officer)

                                 Page 15 of 15