<PAGE>
 
                       SECURITIES AND EXCHANGE COMMISSION

                            Washington, D. C.  20549

                                  FORM 10-QSB
 
[X] Quarterly Report under Section 13 or 15(d) of the Securities Exchange Act of
    1934 for the Quarterly Period ended
    MARCH 31, 1998 or
    --------------

[ ] 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:       1-3753
                       ---------------------------------------------------------
                                        
                        UNITED PARK CITY MINES COMPANY
--------------------------------------------------------------------------------
       (exact name of small business issuer as specified in its charter)


            Delaware                                       87-0219807
------------------------------------------  ------------------------------------
(State or other jurisdiction of                       (I.R.S. Employer
incorporation or organization.)                       Identification No.)

    P. O. Box 1450, Park City, Utah                          84060
------------------------------------------  ------------------------------------
(Address of principal executive offices)                   (Zip Code)

                                (801) 649-8011
--------------------------------------------------------------------------------
                          (Issuer's telephone number)


Check whether the issuer (1) filed all reports required to be filed by Section
13 or 15(d) of the Exchange Act during the past 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     .
     ---     --- 

                    (APPLICABLE ONLY TO CORPORATE ISSUERS)

State the number of shares outstanding of each of the issuer's classes of common
equity, as of the latest practicable date:   3,249,411, as of May 11, 1998.

Transitional Small Business Disclosure Format (check one):  Yes     ; No  X .
                                                                ----     --- 
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1998
                                                                          Page 2

                         PART I - FINANCIAL INFORMATION
                UNITED PARK CITY MINES COMPANY AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEET
                                  (Unaudited)

<TABLE>
<CAPTION>
                                                                                                       March 31,
                                                                                                         1998
                                                                                               -------------------------
ASSETS:
<S>                                                                                            <C>
Cash and cash equivalents............................................................                 $3,140,487
Accounts receivable..................................................................                    172,990
Prepaid expenses.....................................................................                    148,004
Inventories..........................................................................                    196,602
Deferred income taxes................................................................                    475,202
Other................................................................................                     11,100
                                                                                               -------------------------
                                                                                                       4,144,385
                                                                                               -------------------------

Real Estate:
  Hidden Meadows development.........................................................                  1,349,006
  Deferred development costs.........................................................                  1,410,740
                                                                                               -------------------------
                                                                                                       2,759,746
                                                                                               -------------------------
Property and Equipment:
  Mine shaft, buildings and equipment................................................                  4,085,848
  Mine tour attraction...............................................................                  4,830,439
  Construction-in-progress...........................................................                    225,436
  Resort facilities..................................................................                     58,077
  Less accumulated depreciation......................................................                 (4,550,793)
                                                                                               -------------------------
                                                                                                       4,649,007
                                                                                               -------------------------

  Land less accumulated depletion of $1,062,190......................................                 12,795,003
  Water rights.......................................................................                    400,000
                                                                                               -------------------------
                                                                                                      13,195,003
                                                                                               -------------------------

Total assets.........................................................................                $24,748,141
                                                                                               =========================
</TABLE>
  The accompanying notes are an integral part of the consolidated financial 
                                  statements.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1998
                                                                          Page 3


                UNITED PARK CITY MINES COMPANY AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEET
                                  (Unaudited)

<TABLE>
<CAPTION>
                                                                                                         March 31,
                                                                                                           1998
                                                                                               --------------------------
LIABILITIES AND STOCKHOLDERS' EQUITY:
<S>                                                                                    <C>
Accounts payable.....................................................................                  $  210,235
Accrued liabilities..................................................................                     820,747
                                                                                               --------------------------
  Total liabilities..................................................................                   1,030,982
                                                                                               --------------------------

Stockholders' equity:
  Common stock, $.01 par value:
   Authorized:  3,750,000 shares
   Issued:  3,249,411 shares.........................................................                     32,494
  Capital in excess of par value.....................................................                 41,992,798
  Accumulated deficit................................................................                (18,124,349)
                                                                                               -------------------------- 
                                                                                                     23,900,943
  Less cost of treasury stock - 1,294 shares.........................................                  (183,784)
                                                                                               --------------------------
  Total stockholders' equity.........................................................                 23,717,159
                                                                                               -------------------------- 
Total liabilities and stockholders' equity...........................................               $ 24,748,141
                                                                                               ==========================
</TABLE>
  The accompanying notes are an integral part of the consolidated financial 
                                  statements.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1998
                                                                          Page 4


                UNITED PARK CITY MINES COMPANY AND SUBSIDIARIES
                      CONSOLIDATED STATEMENT OF OPERATIONS
                                  (Unaudited)


<TABLE>
<CAPTION>
                                                                                        For Three Months Ended
                                                                                 ------------------------------------
                                                                                     March 31,           March 31,
                                                                                       1998                1997
                                                                                 ----------------    ----------------
<S>                                                                             <C>                     <C>
Revenues:
 Lot sales..........................................................             $  705,000              $  185,000
 Mine tour attraction...............................................                276,477                 292,651
 Interest...........................................................                 34,899                   6,210
 Royalties and rentals..............................................                 93,250                  98,625
 Contract services..................................................                 47,925                  43,716
 Other..............................................................                  2,949                   4,573
                                                                                 ----------------    ----------------
                                                                                  1,160,500                 630,775
                                                                                 ----------------    ----------------
 
Expenses:
 Cost of lot sales and selling expenses.............................                417,568                 114,376
 Mine tour attraction...............................................                355,201                 380,832
 General and administrative costs...................................                234,984                 264,752
 Mine maintenance and administrative costs..........................                263,259                 278,839
 Contract services costs............................................                 40,545                  36,430
 Depreciation.......................................................                130,274                 123,831
 Interest...........................................................                 14,074                  28,312
                                                                                 ----------------    ----------------
                                                                                  1,455,905               1,227,372
                                                                                 ----------------    ----------------
 
Loss before income tax..............................................               (295,405)               (596,597)
 
 Income tax expense.................................................                      0                       0
                                                                                 ----------------    ---------------- 
Net loss............................................................             $ (295,405)             $ (596,597)
                                                                                 ================    ================ 
Basic and diluted net loss per share................................                 $(0.09)                 $(0.22)
                                                                                 ================    ================  
Weighted average number of shares outstanding.......................              3,138,508               2,701,544
                                                                                 ================    ================ 
</TABLE>
  The accompanying notes are an integral part of the consolidated financial 
                                  statements.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1998
                                                                          Page 5


                UNITED PARK CITY MINES COMPANY AND SUBSIDIARIES
                      CONSOLIDATED STATEMENT OF CASH FLOWS
                                  (Unaudited)
<TABLE>
<CAPTION>
                                                                                      For Three Months Ended
                                                                              ---------------------------------------
                                                                                 March 31,               March 31,
                                                                                    1998                    1997
                                                                              ----------------         --------------
<S>                                                                           <C>                      <C>
Cash flows from operating activities:
  Net loss..........................................................             $ (295,405)             $ (596,597)
                                                                              ----------------         --------------
  Adjustments to reconcile net loss to net
  cash used by operating activities:
     Depreciation...................................................                130,273                 123,830
     Increase (decrease) from changes in:
      Accounts receivable...........................................                (76,969)                (94,941)
      Prepaid expenses and inventory................................                 40,957                  34,040
      Hidden Meadow development costs...............................                331,944                  90,825
      Deferred development costs-other..............................               (202,809)                (13,565)
      Accounts payable and accrued liabilities......................                (33,383)               (423,743)
      Contracts payable.............................................                (65,000)
                                                                              ----------------         --------------
          Total adjustments.........................................                125,013                (283,554)
                                                                              ----------------         --------------
Net cash used by operating activities...............................               (170,392)               (880,151)
                                                                              ----------------         --------------
 
Cash flows from investing activities:
  Construction-in-progress..........................................                 (5,244)                 13,975
  Capital expenditures..............................................                 (7,862)                (23,434)
                                                                              ----------------         --------------
Net cash used by investing activities...............................                (13,106)                 (9,459)
                                                                              ----------------         --------------
 
Cash flows from financing activities:
  Costs related to issuing stock for land...........................                (36,893)
  Proceeds from bank note payable...................................                                          1,996
  Principal payments on bank note payable...........................                                        (92,500)
                                                                              ----------------         --------------
Net cash used by financing activities...............................                (36,893)                (90,504)
                                                                              ----------------         --------------
 
Net decrease in cash and cash equivalents...........................               (220,391)               (980,114)
Cash and cash equivalents-beginning of period.......................              3,360,878               1,050,405
                                                                              ----------------         --------------
Cash and cash equivalents-end of period.............................              3,140,487              $   70,291
                                                                              ================         ==============
</TABLE>
  The accompanying notes are an integral part of the consolidated financial 
                                  statements.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1998
                                                                          Page 6

UNITED PARK CITY MINES COMPANY AND SUBSIDIARIES
SELECTED NOTES TO CONSOLIDATED FINANCIAL STATEMENTS(UNAUDITED)
--------------------------------------------------------------------------------

NOTE 1  CONDENSED FINANCIAL STATEMENTS

A.  Disclosure

Certain information and footnote disclosures normally included in financial
statements prepared in accordance with generally accepted accounting principles
have been condensed or omitted.  It is suggested that these financial statements
be read in conjunction with the 1997 Annual Report on Form 10-KSB of United Park
City Mines Company (hereinafter "United Park" or "the Company" or "the
Registrant").

B.  Management's Representation

The consolidated balance sheet as of March 31, 1998 and the consolidated
statements of operations and cash flows for the three month periods ended March
31, 1998 and 1997 have been prepared by the Registrant, without audit.  In the
opinion of management, all adjustments (which include only normal recurring
adjustments) necessary to present fairly the financial position, results of
operations, and cash flows at March 31, 1998 and for all periods presented have
been made.

NOTE 2  IMPACT OF RECENTLY ISSUED ACCOUNTING STANDARDS

In June of 1997, the Financial Accounting Standards Board issued Statement of
Financial Accounting Standards 130, Reporting Comprehensive Income.  The
Statement establishes standards for reporting and display of comprehensive
income and its components (revenues, expenses, gains and losses) in a full set
of general-purpose financial statements.  This Statement is effective for fiscal
years beginning after December 15, 1997.  Because the Company has no items of
comprehensive income, the adoption of this Statement did not have a material
effect on its financial statements.

In June of 1997, the Financial Accounting Standards Board issued Statement of
Financial Accounting Standards 131, Disclosures about Segments of an Enterprise
and Related Information.  The Statement establishes standards for the way that
public business enterprises report information about operating segments in
annual financial statements and requires that those enterprises report selected
information about operating segments in interim financial reports issued to
shareholders.  The Statement is effective for periods beginning after December
15, 1997.  The Company believes that the adoption of this Statement will not
have a material effect on its financial statements.

NOTE 3  LAND ACQUISITION

The Company acquired the assets of New Quincy Mining Company and Lucky Bill
Mining Company during the first quarter of 1998. The acquired assets consisted
of approximately 212 acres of land within the area of the Company's Empire
Canyon Resort development (formerly known as the Flagstaff Mountain in Deer
Valley project). The Company exchanged 203,700 shares of its capital stock for
the land.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1998
                                                                          Page 7

MANAGEMENT'S DISCUSSION AND ANALYSIS
OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS
--------------------------------------------------------------------------------

This Form 10-QSB may contain trend information and forward-looking statements
that involve risks and uncertainties.  The actual results of operations of the
Company could differ materially from the Company's historical results of
operations and those discussed in such forward-looking statements as a result of
certain factors set forth in this section and elsewhere in this Form 10-QSB,
including information incorporated by reference.

LIQUIDITY AND CAPITAL RESOURCES

Real Estate
-----------

The Company's wholly owned subsidiary Blue Ledge Corporation (hereinafter "Blue
Ledge") finalized the sale of four lots in the Hidden Meadows subdivision during
the first three months of 1998. Blue Ledge recognized a profit of $287,432 on
gross sales of $705,000.  The cash proceeds from these lot sales were used to
fund some of the Company's operations.

Since the end of the first quarter of 1998, Blue Ledge finalized the sale of one
additional lot in the Hidden Meadows subdivision and has an additional lot under
contract to sell. The cash proceeds from these lot sales will also be used to
fund some of the Company's operations.

During the first quarter of 1998, the Company acquired the assets of New Quincy
Mining Company (hereinafter "New Quincy") and Lucky Bill Mining Company
(hereinafter "Lucky Bill").  The assets of New Quincy and Lucky Bill consisted
of approximately 212 acres of land within the area of the Company's Empire
Canyon Resort development (formerly known as the Flagstaff Mountain in Deer
Valley project).  This acquisition of land should greatly enhance the Company's
development opportunities with the project.   The Company exchanged 203,700
shares of its capital stock for the land (refer to the Form S-3, Amendment No.
1, dated April 8, 1998 filed by the Company with the Securities and Exchange
Commission for a complete description of the transaction).

The Company continues to pursue the approval of its real estate development
project known as Bonanza Mountain Resort and expects Wasatch County to act upon
the Company's request for master plan approval during 1998.

The Company also expects master plan approval from Wasatch County during 1998 of
its twelve lots which adjoin the Deer Crest development project.

Cash Flow Analysis
------------------

The Company's cash balance decreased $220,391 during the first three months of
1998, leaving a cash balance of $3,140,487 as of March 31, 1998.  During the
first quarter of 1998, the Company's operating activities used cash of $170,392
as compared to cash used in 1997 of $880,151.  The Company will use a portion of
the March 31, 1998 cash balance along with a portion of the proceeds from future
real estate sales by Blue Ledge and revenues from its wholly owned subsidiary
Park City Silver Mine Adventure, Inc. (hereinafter "Silver Mine Adventure") to
fund its future operations. The Company believes that its existing capital
resources and cash flows from operations will be sufficient to meet its
anticipated operating requirements for 1998.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1998
                                                                          Page 8

MANAGEMENT'S DISCUSSION AND ANALYSIS
OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS
--------------------------------------------------------------------------------

RESULTS OF OPERATIONS

1998 Compared with 1997
-----------------------

As previously stated under the Liquidity and Capital Resources - Real Estate
section, Blue Ledge sold four lots in the Hidden Meadows subdivision for a
profit of $287,432 or 41% of the gross sales price during the first quarter of
1998.  Blue Ledge sold one lot in the Hidden Meadows subdivision for a profit of
$70,624 or 38% of the gross sales price during the first quarter of 1997.

During the first three months of 1998, the Silver Mine Adventure generated
revenues of $276,477 and incurred $355,201 in expenses as compared to revenues
of $292,651 and expenses of $380,832 for the same period in 1997. The Company
expects increased numbers of visitors to the tour in 1998 as a result of
increased promotions and an increase in summer tourism.  The Company continues
to believe that Silver Mine Adventure will cover its direct operating costs in
the near future and will generate sufficient future net cash flows to recover
the related capitalized costs.

The Company's interest income increased 462% during the first three months of
1998, when compared with the first three months of 1997.  The increase in
interest income is due to larger cash balances available for investment during
1998.

General and administrative expense decreased 6% during 1998, when compared with
1997.  The decrease is primarily due to decreased costs associated with research
on various projects for possible future development and operations.

Charges for depreciation increased 5% during the first three months of 1998 when
compared with the same period in 1997.  This increase is a result of additional
capital assets used in the Silver Mine Adventure being placed in service in
1998.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1998
                                                                          Page 9

                                    PART II.
                               OTHER INFORMATION


ITEM 6.   EXHIBITS AND REPORTS ON FORM 8-K

(a)  Exhibits filed with this Form 10-QSB:

Exhibit 27 - Financial Data Schedule for electronic filers is filed with this
Form 10-QSB pursuant to Item 601(c) of  Regulation S-B.

(b)  Reports on Form 8-K filed during the period covered by this Form 10-QSB:

Registrant filed a Form 8-K with the Securities and Exchange Commission on
February 19, 1998 reporting under Item 2 thereof the purchase of assets of New
Quincy and Lucky Bill and, under Item 7 (a) Financial Statements of Businesses
Acquired of said Form 8-K, the Registrant reported that it was impracticable to
provide the required financial statement at the time the Form 8-K was filed for
the reason that those companies had conducted no active business operations for
at least the past ten years, and it had been many years since either of those
companies had its financial statements audited.  The Registrant further reported
in said Form 8-K that, when completed by Coopers & Lybrand L.L.P., an audit of
the schedule of revenues and expenses of New Quincy for the year ended December
31, 1997 would be filed not later than sixty days after the filing of the
original Form 8-K.

Under the date of March 27, 1998, the Registrant filed Amendment No. 1 to Form
8-K previously filed on February 19, 1998 with the Securities and Exchange
Commission timely submitting therewith the required financial statement pursuant
to Item 7 (a) Financial Statements of Businesses Acquired in connection with the
purchase of assets of New Quincy and Lucky Bill (refer to the above statement).

Registrant filed a Form 8-K with the Securities and Exchange Commission under
the date of April 8, 1998 reporting pursuant to Item 5 thereof additional
purchases of its capital stock by Laborador Partners L.P., Farley Capital L.P.
and Stephen L. Farley.

Registrant filed a Form 8-K with the Securities and Exchange Commission under
the date of April 23, 1998 reporting pursuant to Item 5 thereof additional
purchases of its capital stock by Laborador Partners L.P., Farley Capital L.P.
and Stephen L. Farley.

The above identified reports on Form 8-K are hereby incorporated herein by
reference.
<PAGE>
 
                                                                     Form 10-QSB
                                                  United Park City Mines Company
                                                                  March 31, 1998
                                                                         Page 10

                                   SIGNATURES

In accordance with the requirements of the Exchange Act, the Registrant caused
this report to be signed on its behalf by the undersigned, thereunto duly
authorized.


                         United Park City Mines Company
              -------------------------------------------------
                                  (Registrant)



      /s/ Edwin L. Osika, Jr.                       /s/ Michael R. Samond
---------------------------------------       ---------------------------------
     Edwin L. Osika, Jr.                              Michael R. Samond
      Executive Vice President,                         Controller
      Secretary, and Treasurer                  (Principal Accounting Officer)
  (Principal Financial Officer and
      Duly Authorized Officer)
 
 
Date:  May 14, 1998