<PAGE>   1
                    U.S. SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C. 20549

                                  FORM 10-QSB

<TABLE>
<CAPTION>

(Mark One)

<S>      <C>
 X       QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934
---      For the quarterly period ended:  June 30, 1997  
                                         ----------------

         TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934
---      For the transition period from                 to 
                                        ---------------    ----------------
</TABLE>

                      Commission file number:   33-43317 

                              EASTON BANCORP, INC.          
       (Exact name of small business issuer as specified in its charter)

<TABLE>
              <S>                                                  <C>
                      Maryland                                                  52-1745344       
                  ----------------                                       ------------------------
              (State of incorporation)                             (I.R.S. Employer Identification No.)
</TABLE>

                  501 Idlewild Avenue, Easton, Maryland  21601
                    (Address of principal executive offices)

                                 (410) 819-0300
                          (Issuer's telephone number)

                                 Not Applicable                              
  (Former name, former address and former fiscal year, if changed since last
                                    report)


         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
   -----   -----

         State the number of shares outstanding of each of the issuer's classes
of common equity, as of the latest practicable date:

         On August 8, 1997, 559,328 shares of the issuer's common stock, par
value $.10 per share, were issued and outstanding.

         Transitional Small Business Disclosure Format (check one):
Yes      No  X
   -----   -----
<PAGE>   2
                                     PART I
                             FINANCIAL INFORMATION

ITEM 1.  FINANCIAL STATEMENTS.

                      EASTON BANCORP, INC. AND SUBSIDIARY
                          CONSOLIDATED BALANCE SHEETS
                                  (Unaudited)

<TABLE>
<CAPTION>
                                                                       June 30,        December 31,
                                                                         1997                1996  
                                                                       --------            --------
 <S>                                                                  <C>                 <C>
                                                    ASSETS
 Cash and due from banks                                              $   894,857         $ 1,211,182
 Federal funds sold                                                     4,952,156           2,824,727
 Investment in Federal Home Loan Bank Stock                               124,500             121,600
 Investment securities held-to-maturity (market
   value of $1,248,319 and $1,247,275, respectively)                    1,250,000           1,250,000
 Loans, less allowance for credit losses of
   $348,000 and $332,253, respectively                                 30,928,305          30,062,431
 Premises and equipment, net                                            1,608,895           1,515,354
 Intangible assets, net                                                    46,964              84,503
 Accrued interest receivable                                              215,275             181,009
 Other assets                                                              49,896              44,134
                                                                      -----------         -----------
          Total assets                                                $40,070,848         $37,294,940
                                                                      ===========         ===========

                                    LIABILITIES AND STOCKHOLDERS' EQUITY
 Deposits
   Noninterest-bearing                                                 $2,940,156         $ 1,719,187
   Interest-bearing                                                    32,703,046          31,039,372
                                                                      -----------         -----------
          Total deposits                                               35,643,202          32,758,559
 Accrued interest payable                                                  94,259              93,684
 Securities sold under agreements to repurchase                           450,939             574,328
 Other liabilities                                                         32,534             145,578
                                                                      -----------         -----------
          Total liabilities                                            36,220,934          33,572,149
                                                                      -----------         -----------

 Stockholders' equity
   Common stock, par value $.10 per share;
     authorized 5,000,000 shares, 559,328
     issued and outstanding                                                55,933              55,933
   Additional paid-in-capital                                           5,217,686           5,217,686
   Retained earnings (deficit)                                         (1,423,705)         (1,550,828)
                                                                      -----------         -----------
          Total stockholders' equity                                    3,849,914           3,722,791
                                                                      -----------         -----------
          Total liabilities and stockholders' equity                  $40,070,848         $37,294,940
                                                                      ===========         ===========
</TABLE>

See accompanying Notes to Consolidated Financial Statements.





                                       1
<PAGE>   3
                      EASTON BANCORP, INC. AND SUBSIDIARY
                       CONSOLIDATED STATEMENTS OF INCOME
                                  (Unaudited)

<TABLE>
<CAPTION>
                                                               Three Months Ended                Six Months Ended
                                                                    June 30,                          June 30,       
                                                             ----------------------            ----------------------
                                                                1997           1996            1997             1996 
                                                               ------         ------          -----            ------
 <S>                                                          <C>             <C>           <C>             <C>
 Interest revenue
   Loans, including fees                                      $722,032        $568,155      $1,408,710      $1,126,850
   Investment securities                                        20,778           9,543          39,857          16,012
   Federal funds sold                                           58,020         122,234         106,413         208,072
                                                              --------        --------      ----------      ----------
          Total interest revenue                               800,830         699,932       1,554,980       1,350,934

 Interest expense                                              401,518         386,380         780,810         752,340
                                                              --------        --------      ----------      ----------

          Net interest income                                  399,312         313,552         774,170         598,594

 Provision for loan losses                                      19,608          21,297          41,466          25,096
                                                              --------        --------      ----------      ----------

          Net interest income after
            provision for loan losses                          379,704         292,255         732,704         573,498
                                                              --------        --------      ----------      ----------

 Other operating revenue                                        22,375          33,003          49,516          55,977
                                                              --------        --------      ----------      ----------

 Other expenses
   Salaries and benefits                                       175,217         157,774         349,403         312,012
   Occupancy                                                    19,183          22,030          37,727          41,289
   Furniture and equipment                                      23,629          23,419          48,004          45,123
   Other operating                                             120,683          92,488         219,963         176,827
                                                              --------        --------      ----------      ----------
          Total operating expenses                             338,712         295,711         655,097         575,251
                                                              --------        --------      ----------      ----------

 Net income before income taxes                                 63,367          29,547         127,123          54,224

 Income taxes                                                      -              -              -                -   
                                                              --------        --------      ----------      ----------


 Net income                                                   $ 63,367        $ 29,547      $  127,123      $   54,224
                                                              ========        ========      ==========      ==========

 Earnings per common share                                    $    .10        $    .05      $      .21      $      .09
                                                              ========        ========      ==========      ==========

 Earnings per common share fully diluted                      $    .10        $    .05      $      .21      $      .09
                                                              ========        ========      ==========      ==========
</TABLE>



See accompanying Notes to Consolidated Financial Statements.





                                       2
<PAGE>   4
                      EASTON BANCORP, INC. AND SUBSIDIARY
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                                  (Unaudited)


<TABLE>
<CAPTION>
                                                                                Six Months Ended
                                                                                    June 30,    
                                                                               -----------------
                                                                              1997             1996
                                                                              ----             ----
 <S>                                                                     <C>              <C>
 CASH FLOWS FROM OPERATING ACTIVITIES
   Interest received                                                     $ 1,519,936      $ 1,331,246
   Other revenue received                                                     49,736           55,977
   Cash paid for operating expenses                                         (687,913)        (479,450)
   Interest paid                                                            (780,235)        (753,065)
                                                                         -----------      -----------
                                                                             101,524          154,708
                                                                         -----------      -----------
 CASH FLOWS FROM INVESTING ACTIVITIES
   Cash paid for premises, equipment and software                           (142,211)          (4,828)
   Net loans to customers                                                 (1,266,329)        (300,175)
   Loan participations purchased                                               -             (100,000)
   Loan participations sold                                                  359,766            -
   Proceeds from sales/maturities of investments                             500,000            -
   Purchase of investment securities                                        (502,900)        (250,000)
   Proceeds from sale of other real estate owned                               -              113,804
                                                                         -----------      -----------

                                                                          (1,051,674)        (541,199)
                                                                         -----------      -----------
 CASH FLOWS FROM FINANCING ACTIVITIES
   Net increase in deposits                                                2,884,643        3,865,183
    Net decrease in securities sold under agreements
     to repurchase                                                          (123,389)         (34,825)
                                                                         -----------      -----------
                                                                           2,761,254        3,830,358
                                                                         -----------      -----------

 NET INCREASE (DECREASE) IN CASH                                           1,811,104        3,443,867

 CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD                          4,035,909        5,491,301
                                                                         -----------      -----------

 CASH AND CASH EQUIVALENTS AT END OF PERIOD                              $ 5,847,013      $ 8,935,168
                                                                         ===========      ===========

 RECONCILIATION OF NET INCOME TO NET CASH PROVIDED
    FROM OPERATING ACTIVITIES
   Net income                                                            $   127,123          $54,224
   Adjustments to reconcile net income to net cash
     provided from operating activities:
        Depreciation and amortization                                         76,461           76,502
        Provision for loan losses                                             41,466           25,096
        Decrease (increase) in accrued interest receivable
           and other assets                                                  (30,279)          (2,742)
        Increase (decrease) in operating accounts payable and
           other liabilities                                                (112,469)           7,076
        Deferred loan origination fees                                          (778)          (1,387)
        Gain on sale of other real estate                                       -              (4,061)
                                                                         -----------      -----------

                                                                         $   101,524      $   154,708
                                                                         ===========      ===========
 Noncash activity:
   Other real estate acquired through foreclosure                        $      -         $   109,743
                                                                         ===========      ===========
</TABLE>


See accompanying Notes to Consolidated Financial Statements.





                                       3
<PAGE>   5

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS:

1.       Basis of Presentation

         The accompanying unaudited condensed financial statements have been
prepared in accordance with generally accepted accounting principles for
interim financial information and with the instructions to Form 10-QSB and Item
310(b) of Regulation S-B of the Securities and Exchange Commission.
Accordingly, they do not include all the information and footnotes required by
generally accepted accounting principles for complete financial statements.  In
the opinion of management, all adjustments (consisting of normal recurring
accruals) considered necessary for a fair presentation have been included.
Operating results for the six months ended June 30, 1997, are not necessarily
indicative of the results that may be expected for the year ended December 31,
1997.  For further information, refer to the consolidated financial statements
and footnotes thereto for the Company's fiscal year ended December 31, 1996,
included in the Company's Form 10-KSB for the year ended December 31, 1996.

2.       Cash Flows

         For purposes of reporting cash flows, cash and cash equivalents
include cash on hand, unrestricted amounts due from banks, overnight
investments in repurchase agreements, and federal funds sold.

3.       Adoption of New Accounting Principles

         During the first quarter of 1997, the Company adopted Financial
Accounting Standards Board Statement No. 125 "Accounting for Transfers and
Servicing of Financial Assets and Extinguishments of Liabilities."  Under this
principle, financial assets are recognized based on the assets the Company
controls and are removed from the balance sheet when control is surrendered.
Liabilities are recorded when incurred.





                                       4
<PAGE>   6

ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
RESULTS OF OPERATIONS.

         Easton Bancorp, Inc. (the "Company") was incorporated in Maryland on
July 19, 1991, primarily to own and control all of the capital stock of Easton
Bank & Trust Company (the "Bank") upon its formation.  The Bank commenced
business on July 1, 1993, and the only activity of the Company since then has
been the ownership and operation of the Bank.  The Bank conducts a general
commercial banking business in its service area, emphasizing the banking needs
of individuals and small- to medium-sized businesses and professional concerns.

         The following discussion of the financial condition and results of
operations of the Company should be read in conjunction with the Company's
financial statements and related notes and other statistical information
included elsewhere herein.

Results of Operations

         Net income for the Company for the three months ended June 30, 1997,
was $63,367, compared to $29,547 during the corresponding period of 1996.  Net
income for the six months ended June 30, 1997, was $127,123, compared to
$54,224 for the corresponding period of 1996.  The increase in net income can
be attributed primarily to the increase in net interest income primarily as a
result of the increase in the Bank's loan portfolio from $24,504,498 at June
30, 1996, to $30,928,305 at June 30, 1997.

         The Bank's provision for loan losses was $19,608 for the quarter ended
June 30, 1997, and $41,466 for the six months ended June 30, 1997, compared to
$21,297 for the quarter ended June 30, 1996, and $25,096 for the six months
ended June 30, 1996.  The allowance for loan losses was $348,000 at June 30,
1997, or 1.11% of total loans, compared to $329,000 at March 31, 1997, or 1.10%
of total loans, and $332,253 at December 31, 1996, or 1.09% of total loans.
Management believes that the allowance for loan losses reflects an amount that
is more than adequate to cover future losses in the loan portfolio; however,
there can be no assurance that loan losses in future periods will not exceed
the allowance for loan losses or that additional increases in the allowance
will not be required.

         Noninterest expense increased $43,001 to $338,712 for the quarter
ended June 30, 1997, from $295,711 for the quarter ended June 30, 1996.  The
increase was primarily related to the increase in other operating expenses of
$28,195, and increases in salaries and benefits of $17,443.  The increase in
other operating expenses for the three months ended June 30, 1997, compared to
the same period for 1996 was primarily due to increased expenses in legal fees
of $5,975, consultants of $3,583, donations of $2,610, data processing of
$2,034 and entertainment of $4,398.  Also, effective April 1997 all directors
are paid $25 for each committee meeting they attend.  This accounted for an
increase in director fees of $2,600 for the quarter end June 30, 1997, from
quarter end June 30, 1996.  The increase in salaries and benefits was due to
annual salary increases, the accrual of bonuses for employees and officers, and
two new employees hired in June 1997.

         Return on average assets and average equity, on an annualized basis,
for the quarter ended June 30, 1997, were .64% and 6.66%, respectively,
compared to .33% and 3.33%, respectively, for the same quarter of 1996.  Return
on average assets and average equity, on an annualized basis, for the six
months ended June 30, 1997, were .66% and 6.71%, respectively.  Earnings per
share on a fully diluted basis for the quarter and the six months ended June
30, 1997, were $.10 and $.21, respectively, compared to $.05 and $.09,
respectively, for the same periods of 1996.

         The Company's assets ended the second quarter of 1997 at $40.1
million, an increase of $2.8 million, or 7.4%, from $37.3 million at December
31, 1996.  This increase can be attributed primarily





                                       5
<PAGE>   7

to the increase in the Bank's deposits which contributed significantly to the
$2.1 million increase in federal funds sold.  Total deposits ended the quarter
at $35.6 million, up 8.8% from $32.8 million at December 31, 1996.  At June 30,
1997, the Company's loan to deposit ratio was 86.8%, compared to 91.8% at
December 31, 1996.

         Management expects that its 1997 income will exceed expenses.  The net
income of $127,123 for the six months ended June 30, 1997, is the largest
profit shown for any six month period since the Bank opened in July 1993. The
growth of loans and deposits and the associated increase in net interest income
are the primary reasons for the increased income.  Although management expects
that the Company's current profitably will continue, future events, such as an
unanticipated deterioration in the loan portfolio, could reverse this trend.
Management's expectations are based on management's best judgement and actual
results will depend on a number of factors that cannot be predicted with
certainty, and thus fulfillment of management's expectations cannot be assured.

Liquidity and Sources of Capital

         The $2.9 million increase in deposits from December 31, 1996, to June
30, 1997, is primarily reflected in the $2.1 million increase in federal funds
sold.  The Company's primary source of liquidity is cash on hand plus
short-term investments.  At June 30, 1997, the Company's liquid assets totaled
$7.2 million, or 18.0% of total assets, compared to $5.4 million, or 14.5% of
total assets, at December 31, 1996.  The Company has a $3,500,000 secured line
of credit with the Federal Home Loan Bank of Atlanta, a $1,000,000 line of
credit, secured by investment securities of the Bank, from a correspondent
bank, and a $1,000,000 unsecured line of credit from another correspondent
bank, all for future liquidity.  If additional liquidity is needed, the Bank
will sell participations in its loans.

         The capital of the Company and the Bank exceeded all prescribed
regulatory capital guidelines at June 30, 1997.  At June 30, 1997, the Tier 1
leverage ratio for the Bank was 9.63%.  At June 30, 1997, the Bank had a
risk-weighted total capital ratio of 13.95%, and a Tier 1 risk-weighted capital
ratio of 12.76%.  The Company expects that its current capital and short-term
investments will satisfy the Company's cash requirements for the foreseeable
future.  However, no assurance can be given in this regard as rapid growth,
deterioration in the loan quality or poor earnings, or a combination of these
factors, could change the Company's capital position in a relatively short
period of time.

                                    PART II
                               OTHER INFORMATION

ITEM 1.  LEGAL PROCEEDINGS.

         There are no material pending legal proceedings to which the Company
or the Bank is a party or of which any of their property is the subject.

ITEM 2.  CHANGES IN SECURITIES.

         Not applicable.

ITEM 3.  DEFAULTS UPON SENIOR SECURITIES.

         Not applicable.





                                       6
<PAGE>   8

ITEM 4.  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

         The Company held its Annual Meeting of Shareholders on May 14, 1997,
at which meeting all five of management's nominees for the Board of Directors
were reelected, including four nominees who were reelected to serve as Class
III Directors for three year terms and one nominee who was elected for a two
year term to fill a vacancy resulting from a newly created Class II
directorship.  The individuals reelected as Class III Directors were: Jack H.
Bishop, receiving 302,569 votes for and 1,550 votes against or withheld, with
no votes abstaining; David F. Lesperance, receiving 302,969 votes for and 1,150
votes against or withheld, with no votes abstaining; Vinodrai Mehta, receiving
302,919 votes for and 1,200 votes against or withheld, with no votes
abstaining; and Jerry L. Wilcoxon, receiving 303,119 votes for and 1,000 votes
against or withheld, with no votes abstaining.  The individual elected to fill
the Class II directorship vacancy was J. Parker Callahan, Jr., receiving
303,119 votes for and 1,000 votes against or withheld, with no votes
abstaining.  Class I and Class II Directors continuing in office are: Sheila W.
Bateman, J. Fredrick Heaton, William C. Hill, W. David Hill, Thomas P. McDavid,
Roger A Orsini and Mahmood S. Shariff.

ITEM 5.  OTHER INFORMATION.

         None.

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K.

         (a)     Exhibits.

<TABLE>
                 <S>      <C>
                 3.1      Articles of Incorporation of the Company (incorporated by reference to Exhibit 3.1 of
                          Registration Statement on Form S-18, File No. 33-43317).

                 3.2      Bylaws of the Company (incorporated by reference to Exhibit 3.2 of Registration Statement on
                          Form S-18, File No. 33-43317).

                 10.1     Employment Agreement dated July 22, 1991, between the Company and Thomas P. McDavid
                          (incorporated by reference to Exhibit 10.1 of Registration Statement on Form S-18, File No. 33-
                          43317).

                 10.2     Easton Bancorp, Inc. 1991 Stock Option Plan (incorporated by reference to Exhibit 10.2 of
                          Registration Statement on Form S-18, File No. 33-43317).

                 10.3     Form of Warrant Agreement (incorporated by reference to Exhibit 10.3 of Registration Statement
                          on Form S-18, File No. 33-43317).

                 11       Computation of Earnings Per Share.

                 27       Financial Data Schedule (for SEC use only).
</TABLE>

         (b)     Reports on Form 8-K.

                 There were no reports on Form 8-K filed by the Company during
the quarter ended June 30, 1997.





                                       7
<PAGE>   9

                                   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.

<TABLE>
<S>      <C>                                                <C>
                                                              EASTON BANCORP, INC.                      
                                                            --------------------------------------------
                                                                    (Registrant)



Date:    August 11, 1997                                    By:  /s/ Thomas P. McDavid                         
       -------------------                                      -----------------------------------------------
                                                                    Thomas P. McDavid
                                                                    President



Date:    August 11, 1997                                    By:  /s/ Pamela A. Mussenden                       
       -------------------                                      -----------------------------------------------
                                                                    Pamela A. Mussenden
                                                                    Assistant Treasurer
                                                                    (Principal Financial Officer)
</TABLE>





                                       8
<PAGE>   10


                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
Exhibit                                                                                                      Sequential
Number                                                 Description                                            Page Number
------                                                 -----------                                            -----------
<S>              <C>
3.1              Articles of Incorporation of the Company (incorporated by reference to Exhibit 3.1 of
                 Registration Statement on Form S-18, File No. 33-43317).

3.2              Bylaws of the Company (incorporated by reference to Exhibit 3.2 of Registration
                 Statement on Form S-18, File No. 33-43317).

10.1             Employment Agreement dated July 22, 1991, between the Company and Thomas P. McDavid
                 (incorporated by reference to Exhibit 10.1 of Registration Statement on Form S-18,
                 File No. 33-43317).

10.2             Easton Bancorp, Inc. 1991 Stock Option Plan (incorporated by reference to Exhibit 10.2
                 of Registration Statement on Form S-18, File No. 33-43317).

10.3             Form of Warrant Agreement (incorporated by reference to Exhibit 10.3 of Registration
                 Statement on Form S-18, File No. 33-43317).

11               Computation of Earnings Per Share.

27               Financial Data Schedule (for SEC use only).
                                                            
</TABLE>