<PAGE>   1





                   U.S. SECURITIES AND EXCHANGE COMMISSION
                           WASHINGTON, D.C.  20549

                                 FORM 10-QSB

(Mark One)


X    QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES
---  EXCHANGE ACT OF 1934
     For the quarterly period ended:  March 31, 1997
                                      --------------                            

___  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:   33-43317

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


                 Maryland                      52-1745344
         ------------------------  ------------------------------------
         (State of incorporation)  (I.R.S. Employer Identification No.)


                  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 May 2, 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>
                                                       March 31,    December 31,
                                                         1997           1996
                                                   -------------     -----------
<S>                                                  <C>             <C>
                                    ASSETS
Cash and due from banks                              $ 1,423,538     $ 1,211,182
Federal funds sold                                     4,587,969       2,824,727
Investment in Federal Home Loan Bank stock               124,500         121,600
Investment securities held-to-maturity (market
  value of $1,242,588 and $1,247,275, respectively)    1,250,000       1,250,000
Loans, less allowance for credit losses of
  $329,000 and $332,253, respectively                 29,893,602      30,062,431
Premises and equipment, net                            1,495,565       1,515,354
Intangible assets, net                                    58,705          84,503
Accrued interest receivable                              211,840         181,009
Other assets                                              60,401          44,134
                                                     -----------     -----------
 Total assets                                        $39,106,120     $37,294,940
                                                     ===========     ===========
                     LIABILITIES AND STOCKHOLDERS' EQUITY
Deposits
 Noninterest-bearing                                 $ 2,551,468     $ 1,719,187
 Interest-bearing                                     31,838,858      31,039,372
                                                     -----------     -----------
  Total deposits                                      34,390,326      32,758,559
Accrued interest payable                                  95,298          93,684
Securities sold under agreements to repurchase           814,575         574,328
Other liabilities                                         19,374         145,578
                                                     -----------     -----------
  Total liabilities                                   35,319,573      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)                           (1,487,072)     (1,550,828)
                                                     -----------     -----------
  Total stockholders' equity                           3,786,547       3,722,791
                                                     -----------     -----------
  Total liabilities and stockholders' equity         $39,106,120     $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
                                                    March 31,
                                                 ----------------
                                                1997          1996
                                                ----          ----
<S>                                          <C>           <C>
Interest revenue
 Loans, including fees                       $686,678      $558,695
 Investment securities                         19,079         6,469
 Federal funds sold                            48,393        85,838
                                             --------      --------
    Total interest revenue                    754,150       651,002
Interest expense                              379,292       365,960
                                             --------      --------
    Net interest income                       374,858       285,042
Provision for loan losses                      21,858         3,799
                                             --------      --------
    Net interest income after
    provision for loan losses                 353,000       281,243
                                             --------      --------
Other operating revenue                        29,126        22,974
                                             --------      --------
Other expenses
 Salaries and benefits                        174,186       154,238
 Occupancy                                     20,529        19,259
 Furniture and equipment                       24,375        21,704
 Other operating                               99,280        84,339
                                             --------      --------
 Total operating expenses                     318,370       279,540
                                             --------      --------
Net income before income taxes                 63,756        24,677
Income taxes                                        -             -
                                             --------      --------
Net income                                   $ 63,756      $ 24,677
                                             ========      ========
Earnings per common share                    $   0.11      $   0.04
                                             ========      ========
Earnings per common share fully diluted      $   0.11      $   0.04
                                             ========      ========
</TABLE>

See accompanying Notes to Consolidated Financial Statements.

                                      2
<PAGE>   4



                     EASTON BANCORP, INC. AND SUBSIDIARY
                    CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (Unaudited)
<TABLE>
<CAPTION>                                                     Three Months Ended
                                                                   March 31,
                                                              -----------------
                                                              1997          1996
                                                              ----          ----
<S>                                                         <C>            <C>
             
CASH FLOWS FROM OPERATING ACTIVITIES                            
                                                           
 Interest received                                          $  722,286     $  656,075
 Other revenue received                                         29,346         22,974
 Cash paid for operating expenses                             (410,649)      (234,466)
 Interest paid                                                (377,678)      (360,346)
                                                            ----------     ---------- 
                                                               (36,695)        84,237
                                                            ----------     ----------
CASH FLOWS FROM INVESTING ACTIVITIES
 Cash paid for premises and equipment                           (4,825)        (3,832)
 Net loans to customers                                         36,209        665,116
 Investment securities purchased                              (502,900)             -
 Proceeds from sales/maturities of investments                 500,000              -
 Loan participations purchased                                     -         (104,346)
 Loan participations sold                                      111,795              -
                                                            ----------     ---------- 
                                                               140,279        556,938
                                                            ----------     ---------- 
CASH FLOWS FROM FINANCING ACTIVITIES
 Net change in customer deposits                             1,631,767      3,805,838
 Net change in securities sold under agreements to
  repurchase                                                   240,247         39,236
                                                            ----------     ---------- 
                                                             1,872,014      3,845,074
                                                            ----------     ---------- 

NET INCREASE IN CASH                                         1,975,598      4,486,249
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD             4,035,909      5,491,301
                                                            ----------     ---------- 
CASH AND CASH EQUIVALENTS AT END OF PERIOD                  $6,011,507     $9,977,550
                                                            ==========     ========== 
RECONCILIATION OF NET INCOME TO NET CASH
 PROVIDED (USED) IN OPERATING ACTIVITIES
 Net income                                                 $   63,756     $   24,677
 Adjustments to reconcile net income to net cash
  provided (used) in operating activities:
   Depreciation and amortization                                38,543         24,341
   Provision for loan losses                                    21,858          3,799
   Decrease (increase) in accrued interest receivable
       and other assets                                        (35,229)         8,645
   Increase (decrease) in operating accounts payable and
        other liabilities                                     (124,590)        26,347
   Deferred loan origination fees                               (1,033)        (3,572)
                                                            ----------     ---------- 
                                                            $  (36,695)    $   84,237
                                                            ==========     ========== 
Noncash activity:
 Other real estate acquired through foreclosure             $        -     $  110,079
                                                            ==========     ========== 
</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 three months ended March 31, 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 March 31, 1997, was
$63,756, compared to $24,677 during the corresponding period of 1996.  This
increase in earnings can be attributed primarily to the increase in net
interest income.  The increase in net interest income is primarily the result
of the increase in the Bank's loan portfolio from $23,566,699 at March 31,
1996, to $29,893,602 at March 31, 1997.

     The Bank's provision for loan losses was $21,858 for the quarter ended
March 31, 1997, compared to $3,799 for the quarter ended March 31, 1996.  The
allowance for loan losses was $329,000 at March 31, 1997, or 1.10% of total
loans, compared to $332,253 at December 31, 1996, or 1.09% of total loans.  The
level of the allowance for loan losses represents management's current estimate
of 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 $38,830, or 13.9%, to $318,370 for the
quarter ended March 31, 1997, from $279,540 for the quarter ended March 31,
1996.  This increase was primarily related to the increase in salaries and
benefits of $19,948.  This increase in salaries and benefits was primarily due
to two part-time positions becoming full-time positions in the second half of
1996.  The increase in salaries and benefits expenses was also due to annual
salary increases and the accrual of bonuses for employees and officers.  In
addition to the increase in salaries and benefits, other operating expenses
increased $14,941, which included increases in advertising expenses of $4,781,
data processing expenses of $2,875 and legal fees of $4,272.

     Return on average assets and average equity, on an annualized basis, for
the quarter ended March 31, 1997, were .77% and  7.95%, respectively, compared
to .31% and 2.81%, respectively, for the same quarter of 1996.  Earnings per
share on a fully diluted basis for the quarters ended March 31, 1997, and March
31, 1996, amounted to $0.11 and $0.04, respectively.

     The Company's assets ended the first quarter of 1997 at $39.1 million, an
increase of 4.9% from $37.3 million at December 31, 1996.  This increase can be
attributed primarily to the increase in the Bank's deposits which resulted in
the $1.8 million increase in federal funds sold.  Total deposits ended the
quarter at $34.4 million, up 5.0% from $32.8 million at December 31, 1996.  At
March 31, 1997, the Company's loan to deposit ratio was 86.9%, compared to
91.8% at December 31, 1996.

                                      5
<PAGE>   7




     Management expects that its 1997 income will exceed expenses.  The net
income of $63,756 for the quarter ended March 31, 1997, represented another
strong quarter for the Company.  Net interest income (before the provision for
loan losses) of $374,858 is the largest margin for any quarter since the Bank
opened in July 1993.  The growth of loans and deposits are the primary reasons
for the increase in net interest 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 $1.6 million increase in deposits from December 31, 1996, to March 31,
1997, is primarily reflected in the $1.8 million increase in federal funds
sold.  The Company's primary source of liquidity is cash on hand plus
short-term investments.  At March 31, 1997, the Company's liquid assets totaled
$7,386,007, or 18.9% of total assets, compared to $5,407,509, or 14.5% of total
assets, at December 31, 1996.  The Company has a $1,000,000 line of credit,
secured by investment securities of the Bank, from a correspondent bank for
future liquidity, and a $3,500,000 unsecured line of credit with the Federal
Home Loan Bank of Atlanta.  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 March 31, 1997.  At March 31, 1997, the Tier 1 leverage
ratio for the Bank was 9.71%.  At March 31, 1997, the Bank had a risk-weighted
total capital ratio of 14.17%, and a Tier 1 risk-weighted capital ratio of
12.99%.  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.

     There were no matters submitted to security holders for a vote during the
quarter ended March 31, 1997.

ITEM 5.  OTHER INFORMATION.

     None.

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

     (a) Exhibits.

         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).

         11.1   Computation of Earnings Per Share.

         27.1   Financial Data Schedule (for SEC use only).

     (b) Reports on Form 8-K.

               There were no reports on Form 8-K filed by the Company during
          the quarter ended March 31, 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.

                                          EASTON BANCORP, INC.
                                         ---------------------------------
                                              (Registrant)




Date:    May 12, 1997                    By:  /s/ Thomas P. McDavid
        ---------------                       ---------------------------- 
                                                  Thomas P. McDavid
                                                  President




Date:    May 12, 1997                    By:  /s/ Pamela A. Mussenden
        ---------------                       ----------------------------
                                                  Pamela A. Mussenden
                                                  Assistant Treasurer
                                                  (Principal Financial Officer)



                                      8
<PAGE>   10





                              INDEX TO EXHIBITS


Exhibit                                                         Sequential
Number                       Description                        Page Number
-------                      -----------                        -----------


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).

11.1 Computation of Earnings Per Share.

27.1 Financial Data Schedule (for SEC use only).