<PAGE>   1
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                                  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 QUARTER ENDED MARCH 31, 1998

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


                         Commission File Number: 0-20750

                            STERLING BANCSHARES, INC.
             (Exact name of registrant as specified in its charter)


         TEXAS                                                 74-2175590
(State of Incorporation)                                (IRS Employer ID Number)

                       15000 NORTHWEST FREEWAY, SUITE 200
                              HOUSTON, TEXAS 77040
                     (Address of principal executive office)

                                  713-466-8300
                         (Registrant's telephone number)

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 and Exchange Act of 1934
("Act") 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 
                               -----                 -----

The number of shares outstanding of each class of the registrant's capital stock
as of March 31, 1998:

<TABLE>
<CAPTION>
       CLASS OF STOCK                                     SHARES OUTSTANDING
       --------------                                     ------------------
<S>                                                       <C>       
Common Stock, Par Value $1.00                                  20,859,748
</TABLE>


================================================================================


<PAGE>   2



PART I.  FINANCIAL INFORMATION

ITEM I.  CONDENSED FINANCIAL STATEMENTS

                   STERLING BANCSHARES, INC. AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEETS
                                 (In thousands)


<TABLE>
<CAPTION>
                                                                              MARCH 31,       DECEMBER 31,
                                                                                 1998             1997
                                                                             -----------      -----------
                                                                             (UNAUDITED)
<S>                                                                          <C>              <C>        
ASSETS
Cash and due from banks                                                      $    73,762      $   110,479
Federal funds sold                                                                15,000               --
Interest-bearing deposits in financial institutions                                  418              409
Securities purchased with an agreement to resell                                  27,104           15,496
Available-for-sale investment securities, at fair value                           56,463           81,592
Held-to-maturity investment securities, at amortized cost                        171,847          195,309
Investment in Sterling Capital Mortgage Company                                    2,679            2,510
Loans held for sale                                                               94,012           70,193

Loans                                                                            699,091          667,918
Allowance for credit losses                                                       (7,929)          (7,377)
                                                                             -----------      -----------
  Loans, net                                                                     691,162          660,541
Accrued interest receivable                                                        7,157            7,638
Real estate acquired by foreclosure                                                1,314              318
Premises and equipment, net                                                       29,104           29,468
Goodwill, net                                                                      1,459            1,518
Other assets                                                                       5,829            7,406
                                                                             -----------      -----------
TOTAL ASSETS                                                                 $ 1,177,310      $ 1,182,877
                                                                             ===========      ===========

LIABILITIES AND SHAREHOLDERS' EQUITY
Demand deposits:
  Noninterest-bearing                                                        $   335,554      $   342,623
  Interest-bearing                                                               462,946          454,388
Certificates of deposit and other time deposits                                  241,404          225,209
                                                                             -----------      -----------
  Total deposits                                                               1,039,904        1,022,220
Securities sold under agreements to repurchase and other borrowed funds           19,463           44,491
Accrued interest payable and other liabilities                                     5,113            7,432
                                                                             -----------      -----------
  Total liabilities                                                            1,064,480        1,074,143

COMPANY-OBLIGATED MANDITORILY REDEEMABLE
 TRUST PREFERRED SECURITIES OF SUBSIDIARY TRUST                                   28,750           28,750

Shareholders' equity:
  Convertible preferred stock, $1 par value, 1 million shares authorized             177              177
  Common stock, $1 par value, 50 million shares authorized                        20,860           20,686
  Capital surplus                                                                 16,010           14,949
  Retained earnings                                                               47,129           44,287
  Net unrealized gains (losses) on available-for-sale investment
    securities, net of tax                                                           (96)            (115)
                                                                             -----------      -----------
    Total shareholders' equity                                                    84,080           79,984
                                                                             -----------      -----------
TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                                   $ 1,177,310      $ 1,182,877
                                                                             ===========      ===========
</TABLE>



SEE NOTES TO INTERIM CONSOLIDATED FINANCIAL STATEMENTS.


                                       2
<PAGE>   3
                   STERLING BANCSHARES, INC. AND SUBSIDIARIES
                        CONSOLIDATED STATEMENTS OF INCOME
                                 (In thousands)


<TABLE>
<CAPTION>
                                                                THREE MONTHS
                                                               ENDED MARCH 31,
                                                              1998        1997
                                                             -------     -------
                                                                  (Unaudited)
<S>                                                          <C>         <C>    
Interest income:
  Loans, including fees                                      $17,618     $13,548
  Federal funds sold                                              92         347
  Deposits in financial institutions                             153         126
  Securities purchased under agreements to resell                351          --
  Investment securities:
    Taxable                                                    3,685       3,065
    Tax-exempt                                                   211         282
                                                             -------     -------
      Total interest income                                   22,110      17,368

Interest expense:
  Demand and savings deposits                                  3,482       2,949
  Certificates and other time deposits                         2,962       2,341
  Federal funds purchased and securities purchased under
    agreements to resell                                         238          65
  Notes payable                                                   --          94
                                                             -------     -------
      Total interest expense                                   6,682       5,449
                                                             -------     -------
      NET INTEREST INCOME                                     15,428      11,919

        Provision for credit losses                              880         682
                                                             -------     -------
      NET INTEREST INCOME AFTER PROVISION                     14,548      11,237

Noninterest income:
  Customer service fees                                        1,619       1,454
  Equity in earnings of Sterling Capital Mortgage Company        193          --
  Other                                                          806         656
                                                             -------     -------
      Total noninterest income                                 2,618       2,110

Noninterest expenses:
  Salaries and employee benefits                               6,247       5,189
  Occupancy expense                                            1,445       1,334
  Technology                                                     734         457
  Supplies                                                       248         133
  Professional fees                                              273         189
  Minority interest expense                                      667          --
  Other                                                        2,001       1,792
                                                             -------     -------
      Total noninterest expenses                              11,615       9,094

      NET INCOME BEFORE INCOME TAXES                           5,551       4,253
        Provision for income taxes                             1,876       1,404
                                                             -------     -------
      NET INCOME                                             $ 3,675     $ 2,849
                                                             =======     =======
EARNINGS PER SHARE:
  Basic                                                      $  0.18     $  0.14
                                                             =======     =======
  Diluted                                                    $  0.17     $  0.13
                                                             =======     =======
</TABLE>


SEE NOTES TO INTERIM CONSOLIDATED FINANCIAL STATEMENTS.


                                       3
<PAGE>   4
                   STERLING BANCSHARES, INC. AND SUBSIDIARIES
                            STATEMENTS OF CASH FLOWS
                                 (In thousands)


<TABLE>
<CAPTION>
                                                                                            THREE MONTHS ENDED MARCH 31,
                                                                                            ----------------------------
                                                                                               1998            1997 
                                                                                             ---------      ---------
<S>                                                                                          <C>            <C>      
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net income                                                                                 $   3,675      $   2,849
  Adjustments to reconcile net income to net cash (used in) provided by
    operating activities
      Amortization and accretion of premiums and discounts on investment securities, net            89             77
      Equity in undistributed earnings of Sterling Capital Mortgage Company                       (169)            50
      Provision for credit losses                                                                  880            682
      Loss on disposal of premises and equipment                                                    --            118
      Loss on sale of real estate acquired by foreclosure and repossessed assets                    --              2
      Depreciation and amortization                                                              1,168            833
      Net change in loans held for sale                                                        (23,819)        10,936
      Increase (decrease) in accrued interest receivable and other assets                        2,117           (651)
      Decrease in accrued interest payable and other liabilities                                (2,328)          (610)
                                                                                             ---------      ---------
        NET CASH (USED IN) PROVIDED BY OPERATING ACTIVITIES                                    (18,387)        14,286

CASH FLOWS FROM INVESTING ACTIVITIES:
  Increase in securities purchased under agreements to resell                                  (11,608)            --
  Proceeds from maturity and paydowns of held-to-maturity investment securities                 25,182          5,166
  Purchases of held-to-maturity investment securities                                               --        (25,660)
  Proceeds from maturity and paydowns of available-for-sale investment securities               23,429         13,011
  Purchases of available-for-sale investment securities                                            (81)       (13,049)
  Net increase in loans                                                                        (32,654)       (29,590)
  Proceeds from sale of real estate acquired by foreclosure                                        157            405
  Net increase in interest-bearing deposits in financial institutions                               (9)       (25,405)
  Proceeds from sale of premises and equipment                                                      80             29
  Purchase of premises and equipment                                                              (884)        (2,897)
                                                                                             ---------      ---------
        NET CASH (USED IN) PROVIDED BY INVESTING ACTIVITIES                                      3,612        (77,990)

CASH FLOWS FROM FINANCING ACTIVITIES:
  Net increase in deposit accounts                                                              17,684         28,973
  Net increase (decrease) in repurchase agreements/funds purchased                             (25,028)         4,071
  Repayment of notes payable                                                                        --           (400)
  Proceeds from issuance of common stock                                                         1,236            223
  Dividends paid                                                                                  (834)          (662)
                                                                                             ---------      ---------
        NET CASH (USED IN) PROVIDED BY FINANCING ACTIVITIES                                     (6,942)        32,205

NET DECREASE IN CASH AND CASH EQUIVALENTS                                                      (21,717)       (31,499)

CASH AND CASH EQUIVALENTS:
  Beginning of period                                                                          110,479        125,854
                                                                                             ---------      ---------
  End of period                                                                              $  88,762      $  94,355
                                                                                             =========      =========

SUPPLEMENTAL INFORMATION:
  Income taxes paid                                                                          $     422      $     200
                                                                                             =========      =========
  Interest paid                                                                              $   6,648      $   5,395
                                                                                             =========      =========
  Noncash investing and financing activities:
    Acquisitions of real estate through foreclosure of collateral                            $   1,153      $      --
                                                                                             =========      =========
</TABLE>


SEE NOTES TO INTERIM CONSOLIDATED FINANCIAL STATEMENTS.


                                       4
<PAGE>   5



                   STERLING BANCSHARES, INC., AND SUBSIDIARIES
               NOTES TO INTERIM CONSOLIDATED FINANCIAL STATEMENTS
                                 MARCH 31, 1998

1.   BASIS OF PRESENTATION:

     The accompanying unaudited consolidated financial statements have been
     prepared in accordance with generally accepted accounting principles for
     interim financial information and with the rules and regulations of the
     Securities and Exchange Commission. Accordingly, they do not include all of
     the information and notes required by generally accepted accounting
     principles for complete financial statements. In the opinion of management,
     all adjustments (consisting of normal recurring items) considered necessary
     for a fair presentation have been included. Operating results for the three
     month period ended March 31, 1998 are not necessarily indicative of the
     results that may be expected for the year ended December 31, 1998. For
     further information, refer to the consolidated financial statements and
     notes thereto included in the annual report on form 10-K of Sterling
     Bancshares, Inc. (the "Company") for the year ended December 31, 1997.

     On September 30, 1997, the Company acquired First Houston Bancshares, Inc.
     ("First Houston") in an exchange of 1,686,014 shares of the Company's
     common stock for First Houston's outstanding common and preferred stock.
     The transaction was accounted for as a pooling of interests and previously
     issued financial statements were restated.

2.   EARNINGS PER COMMON SHARE

     Earnings per common share was computed based on the following (in
     thousands, except per share amounts):


<TABLE>
<CAPTION>
                                                         QUARTER ENDED MARCH 31,
                                               -------------------------------------------
                                                      1998                   1997
                                               -------------------   ---------------------
                                                AMOUNT   PER SHARE    AMOUNT     PER SHARE
                                               -------   ---------   -------     ---------
<S>                                            <C>       <C>         <C>         <C>
Net income                                     $ 3,675               $ 2,849
                                               =======               =======
Basic:
  Weighted average shares outstanding           20,767     $ 0.18     20,504     $   0.14
                                                           ======                ========
Diluted:
  Add incremental shares for:
    Assumed exercise of outstanding options        741                   696
    Assumed conversion of preferred stock          459                   255
                                               -------               -------
Total                                           21,967     $ 0.17     21,455     $   0.13
                                               =======     ======    =======     ========
</TABLE>

     ----------------------------------------------------------------------
     Note: Net income and share information have been adjusted to reflect a
     three-for-two stock split distributed February 20, 1998.

3.   RECENT ACCOUNTING STANDARDS

     On January 1, 1998, the Company adopted SFAS No. 130, "Reporting
     Comprehensive Income", which requires that all components of comprehensive
     income and total comprehensive income be reported on one of the following:
     (1) the statement of operations, (2) the statement of stockholders' equity
     or (3) a new separate statement of comprehensive income. Comprehensive
     income is 


                                       5
<PAGE>   6

     comprised of net income and all changes to stockholders' equity, except
     those due to investments by owners (changes in capital surplus) and
     distributions to owners (dividends). The Company will report comprehensive
     income on the statement of stockholders' equity. Comprehensive income for
     the Company includes net income and the changes in unrealized gains and
     losses on available-for-sale securities, net of tax. Comprehensive income
     totaled $3,694,000 for the three months ended March 31, 1998.

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

SIGNIFICANT DEVELOPMENTS

EXPANSION - The Company opened its fourteenth banking office in the Cypress
Station area, north of the city, in January 1997.

On September 30, 1997, First Houston was acquired by the Company in a
stock-for-stock merger. On October 27, 1997, Houston National Bank was merged
into Sterling Bank, creating the Bank's fifteenth banking office.

In January 1998, the Company opened its sixteenth banking office on Spencer
Highway in Pasadena. In conjunction with the opening of this office, the
Company's Board approved in April 1998 the offering of 50,000 shares of Series E
convertible preferred stock. These preferred shares will be convertible into a
maximum of 62,500 shares of the Company's common stock. The offering will
terminate on or about July 15, 1998. The conversion ratio is dependent upon the
Spencer Highway office meeting certain performance goals.

On May 13, 1998, the Company opened its seventeenth banking office in Fort Bend
county.

On February 17, 1998, the Company entered into an Agreement and Plan of
Consolidation (the "Agreement") with Humble National Bank ("Humble"). The terms
of the Agreement provide that each share of Humble's common stock will be
canceled and converted to the right to receive a fractional share of the
Company's common stock, for a total of 855,000 shares of the Company's common
stock. Humble had approximately $54.2 million in assets and $49.6 million in
deposits as of December 31, 1997. This Agreement is subject to approval by the
applicable banking regulatory authorities.

FINANCIAL CONDITION

INVESTMENTS IN SUBSIDIARIES - Sterling Bank is a wholly-owned banking
subsidiary. In September 1996, the Company purchased a 40% equity and 44%
voting interest in Sterling Capital Mortgage Company ("SCMC"), an originator and
servicer of single family residential mortgage loans headquartered in Houston,
Texas. The Company also owns a 100% beneficial interest in Sterling Bancshares
Capital Trust I.

TOTAL ASSETS - The total consolidated assets of the Company as of March 31, 1998
were $1.2 billion, as compared to $1.2 billion as of December 31, 1997, a small
decrease of $5.6 million or 0.5%.

FEDERAL FUNDS SOLD - The Bank had federal funds sold of $15.0 million at March
31, 1998. Comparatively, the Bank had no federal funds sold on December 31,
1997.


                                       6
<PAGE>   7

SECURITIES PURCHASED UNDER AGREEMENTS TO RESELL - As of March 31, 1998,
securities purchased under agreements to resell totaled $27.1 million as
compared to $15.5 million as of December 31, 1997. The securities purchased are
SBA guaranteed loan pools and certificates and generally have a term of six
months or less.

INVESTMENT SECURITIES - The Bank's investment portfolio as of March 31, 1998,
totaled $228.3 million, as compared to $276.9 million on December 31, 1997, a
decrease of $48.6 million or 17.6%. Proceeds from maturities, calls and paydowns
on mortgage-backed securities were reinvested into federal funds sold and loans.
The Bank has designated its total securities portfolio into held-to-maturity
("HTM") and available-for-sale ("AFS") categories. As of March 31, 1998, the HTM
portfolio totaled $171.8 million and the AFS portfolio totaled $56.5 million.
The Bank tracks but does not record market changes on its HTM portfolio. At
March 31, 1998, the market value of the HTM portfolio was $174.3 million.

LOANS HELD FOR SALE - Total loans held for sale increased from $70.2 million at
December 31, 1997 to $94.0 million at March 31, 1998, an increase of 33.9%.
Loans held for sale included loans warehoused for Sterling Capital Mortgage
Company of $83.1 million and $61.1 million and student loans of $10.9 million
and $9.1 million at March 31, 1998 and December 31, 1997, respectively. Loans
warehoused for Sterling Capital Mortgage increased by $9.1 million or 14.9% from
December 31, 1997.

LOANS HELD FOR INVESTMENT - As of March 31, 1998, loans held for investment were
$699.1 million. When compared to loans held for investment of $667.9 million on
December 31, 1997, the March 31, 1998 loan balance represents a year-to-date
$31.2 million increase in internal loan production, net of payoffs, or an
increase of 4.7%. At March 31, 1998, loans held for investment as a percentage
of assets and deposits were 59.4% and 67.2%, respectively.

The following table summarizes the Bank's loan portfolio by type of loan as of
March 31, 1998 (in thousands):

<TABLE>
<CAPTION>
                                                         PERCENT OF
                                                           TOTAL
                                                         ----------
<S>                                      <C>             <C>   
Commercial, financial and industrial       279,100          39.92%
Real estate - commercial                   193,856          27.73%
Real estate - residential mortgage          85,342          12.21%
Real estate - construction                  58,628           8.39%
Foreign commercial and industrial              842           0.12%
Installment and other                       82,443          11.79%
  Less unearned discount                    (1,120)         (0.16)%
                                         ---------         ------ 
    Total loans held for investment      $ 699,091         100.00%
                                         =========         ====== 
</TABLE>


                                       7
<PAGE>   8


ALLOWANCE FOR CREDIT LOSSES - Following is a summary of the changes in the
allowance for credit losses for the three months ended March 31, 1998, and the
relationship of the allowance to total loans at March 31, 1998, and December 31,
1997 (in thousands):

<TABLE>
<S>                                                <C>    
Allowance for credit losses, December 31, 1997     $ 7,377
Chargeoffs                                            (413)
Recoveries                                              85
Provision for credit losses                            880
                                                   -------
Allowance for credit losses, March 31, 1998        $ 7,929
                                                   =======
</TABLE>


<TABLE>
<CAPTION>
                                               March 31,    December 31,
                                                 1998           1997
                                               ---------    ------------
<S>                                            <C>            <C>     
Loans held for investment at period-end        $699,091       $667,918
Allowance for credit losses                    $  7,929       $  7,377
Allowance as a percent of period-end loans         1.13%          1.10%
</TABLE>


In order to determine the adequacy of the allowance for credit losses,
management considers the risk classification and delinquency status of loans and
other factors. Management also establishes specific allowances for credits which
management believes require allowances greater than those allocated according to
their risk classification. An unallocated allowance is also established based on
the Bank's historical charge-off experience over the last ten years. The Bank
may reduce the provision for credit losses where appropriate. The Bank will
continue to monitor the adequacy of the allowance for credit losses to determine
the appropriate accrual for the Bank's bad debt expense.

RISK ELEMENTS - Non-performing, past due, and restructured loans are fully or
substantially secured by assets, with any excess of loan balances over
collateral values specifically allocated in the allowance for credit losses.
Eight properties make up the $1.3 million of other real estate owned ("ORE") at
March 31, 1998. One property makes up over half of that balance and was
foreclosed during March 1998. The Bank carries all properties at the current
fair market value, less estimated closing and holding costs.

The Bank defines potential problem loans as those loans not classified as
non-performing, but where information known by management indicates serious
doubt that the borrower will be able to comply with the present payment terms.
Management identifies these loans through its continuous loan review process and
defines potential problem loans as those loans classified as substandard,
doubtful, or loss, excluding all non-performing loans. As of March 31, 1998, the
Bank has no material foreign loans outstanding or loan concentrations. The Bank,
however, continues to monitor the potential risk of foreign borrowers and
concentrations of credit.


                                       8
<PAGE>   9

The following schedule summarizes consolidated non-performing loans,
non-performing assets and potential problem loans at year-end 1997 and at March
31, 1998


<TABLE>
<CAPTION>
                                                     MARCH 31,   DECEMBER 31,
                                                       1998         1997
                                                     ---------   ------------
                                                         (In thousands)
<S>                                                   <C>          <C>    
Nonaccrual loans                                      $ 4,055      $ 4,192
Restructured loans                                         --           --
Accruing loans past due 90 days or more                   302          368
                                                      -------      -------
  Total nonperforming loans                             4,357        4,560
ORE and other foreclosed assets                         1,534          672
                                                      -------      -------
  Total nonperforming assets                          $ 5,891      $ 5,232
                                                      =======      =======
Total nonperforming loans as a % of gross loans          0.55%        0.62%
Total nonperforming assets as a % of total assets        0.50%        0.44%
Potential problem loans                               $12,395      $12,676
                                                      =======      =======
</TABLE>


PREMISES AND EQUIPMENT - The Bank's premises and equipment, net of depreciation,
as of March 31, 1998, were $29.1 million, as compared to $29.5 million as of
December 31, 1997, a decrease of $364 thousand.

DEPOSITS - Total deposits as of March 31, 1998, were $1.04 billion, as compared
to $1.02 billion on December 31, 1997, an increase of $17.7 million, resulting
from growth in same location deposits, combined with the additional deposits of
the new banking office in Pasadena. Non-interest bearing demand deposits at
March 31, 1998, were $335.6 million, as compared to $342.6 million at December
31, 1997, a decrease of $7.1 million or 2.1%. The percentage of non-interest
bearing deposits to total deposits as of March 31, 1998 continued to be strong
at 32.3%.

CAPITAL RESOURCES AND LIQUIDITY

SHAREHOLDERS' EQUITY - The following table displays the changes in shareholders'
equity from December 31, 1997 to March 31,1998 (in thousands):


<TABLE>
<S>                                                      <C>      <C>
Equity, December 31, 1997                                         $ 79,984
Comprehensive income:                         
 Net income                                              3,675
 Net change in net unrealized losses on AFS securities      19
                                                         -----
  Total comprehensive income                                         3,694
Issuance of common stock                                             1,236
Cash dividends paid                                                   (834)
                                                                  --------
Equity, March 31, 1998                                            $ 84,080
                                                                  ========
</TABLE>


The Company's risk based capital ratios remain above the levels designated as
"well capitalized" on March 31, 1998, with Tier-1 Capital, Total Risk-Based
Capital, and Leverage Capital Ratios of 12.07%, 13.01%, and 9.55%, respectively.


                                       9
<PAGE>   10

LIQUIDITY

Effective management of balance sheet liquidity is necessary to fund growth in
earning assets and to pay liability maturities, depository customers' withdrawal
requirements and shareholders' dividends. The Company has instituted
Asset/Liability Management policies, including but not limited to a computer
simulation model, to improve liquidity controls and to enhance its management of
interest rate risk and financial condition. The Company has numerous sources of
liquidity including a significant portfolio of shorter term assets, marketable
investment securities (excluding those presently classified as
"Held-to-maturity"), increases in customers' deposits, and access to borrowing
arrangements. Available borrowing arrangements maintained by the Bank include
informal federal funds lines with other commercial banks, an advancement
arrangement with the Federal Home Loan Bank ("FHLB"), and reverse repurchase
lines with other commercial banks and the FHLB.

RESULTS OF OPERATIONS

NET INCOME - Net income for the three month period ended March 31, 1998, was
$3.7 million as compared to $2.8 million for the same period in 1997, an
increase of approximately $826 thousand or 29.0%. This increase was a result of
the overall growth in the asset base of the bank.

NET INTEREST INCOME - Net interest income for the three month period ended March
31, 1998, was $15.4 million, as compared to $11.9 million for the same period in
1997, an increase of $3.5 million or 29.4%. The growth in net interest income is
attributable primarily to increases in average earning assets, enhanced by the
maintenance of a strong net interest margin. Average earning assets for the
quarter ended March 31, 1998, were $1.04 billion, up $225.0 million, or 27.6%
from $816.4 million for the same period in 1997. The yield on average earning
assets for the three month period ended March 31, 1998, was 8.61%, as compared
to 8.63% for the same period in 1997, a slight decrease of 2 basis points. For
the first three months of 1998, average total loans represented 72.2% of average
total interest earning assets, compared to 68.2% for the same period in 1997.
The cost of interest bearing liabilities rose 12 basis points from 3.71% in 1997
to 3.83% in 1998. Even though average rates on earning assets declined and
average rates on interest bearing liabilities increased, the Company's 6.01% net
interest margin for the first three months of 1998 increased from the 5.92% net
interest margin recorded during the same period in 1997. This is the result of
growth in average non-interest bearing demand deposits of $73.6 million, or
29.3%, reinvestment of earnings and issuance of stock resulting in an increase
of average equity of $13.4 million, or 19.5%, and the issuance of the Trust
Preferred Securities of $28.8 million.

The data used in the analysis of the changes in net interest income is derived
from the daily average levels of earning assets and interest-bearing liabilities
as well as from the rates earned and paid on such amounts. The rates earned and
paid on each major type of asset and liability are shown beside the average
balance in the account for the period. The average yields on all
interest-earning assets and the average cost of all interest-bearing liabilities
also are summarized.


                                       10
<PAGE>   11

The following schedule gives a comparative analysis of the Company's daily
average interest-earning accounts and interest-bearing accounts for the
three-month periods ended March 31, 1998 and 1997:


                           CONSOLIDATED YIELD ANALYSIS
                          THREE MONTHS ENDED MARCH 31,
                             (DOLLARS IN THOUSANDS)


<TABLE>
<CAPTION>
                                                                       1998                                  1997
                                                        --------------------------------    ----------------------------------
                                                         AVERAGE                             AVERAGE
                                                         BALANCE     INTEREST     YIELD      BALANCE       INTEREST    YIELD
                                                        ----------  ----------   -------    ----------    ----------  -------- 
<S>                                                     <C>         <C>          <C>        <C>           <C>         <C>   
INTEREST EARNING ASSETS:
Interest bearing deposits in financial institutions     $   11,057  $      153      5.61%   $   10,448    $      126     4.89%
Federal funds sold                                           6,322          92      5.90%       25,871           347     5.44%
Securities purchased under agreements to resell             20,067         351      7.09%           --            --       --
Investment securities (taxable)                            230,996       3,685      6.47%      201,271         3,065     6.18%
Investment securities (tax-exempt)                          20,806         211      4.11%       22,105           282     5.17%
Loans, net of unearned discount (taxable)                  751,304      17,603      9.50%      555,759        13,531     9.87%
Loans, not of unearned discount (tax-exempt)                   778          15      7.82%          919            17     7.50%
                                                        ----------  ----------   -------    ----------    ----------  ------- 
  Total Interest Earning Assets                          1,041,330      22,110      8.61%      816,373        17,368     8.63%


Noninterest Earning Assets:
Cash and due from banks                                     71,528                              68,867
Premises and equipment, net                                 29,366                              27,456
Other assets                                                22,117                              17,551
Allowance for credit losses                                 (7,542)                             (7,226)
                                                        ----------                          ----------
  Total Noninterest Earning Assets                         115,469                             106,648
                                                        ----------                          ----------

  TOTAL ASSETS                                          $1,156,799                          $  923,021
                                                        ==========                          ==========

INTEREST BEARING LIABILITIES:
Demand and savings deposits                             $  455,960  $    3,482      3.10%   $  395,608    $    2,949     3.02%
Certificates and other time deposits                       232,024       2,962      5.18%      190,415         2,341     4.99%
Other borrowings                                            20,326         238      4.75%        5,955            65     4.43%
Notes payable                                                   --          --        --         3,867            94     9.86%
                                                        ----------  ----------   -------    ----------    ----------  ------- 
  Total Interest Bearing Liabilities                       708,310       6,682      3.83%      595,845         5,449     3.71%

Noninterest Bearing Liabilities:
Demand deposits                                            324,431                             250,833
Other liabilities                                           12,877                               7,354
Trust preferred securities                                  28,750                                  --  
Shareholders' equity                                        82,431                              68,989
                                                        ----------                          ----------
  Total Noninterest Bearing Liabilities                    448,489                             327,176
                                                        ----------                          ----------

  TOTAL LIABILITIES AND SHAREHOLDERS' EQUITY            $1,156,799                          $  923,021
                                                        ==========                          ==========

NET INTEREST INCOME & MARGIN                                        $   15,428      6.01%                 $   11,919     5.92%
                                                                    ==========   =======                  ==========  =======
NET INTEREST INCOME & MARGIN (TAX EQUIVALENT)                       $   15,526      6.05%                 $   12,054     5.99%
                                                                    ==========   =======                  ==========  =======
</TABLE>


PROVISION FOR CREDIT LOSSES - The provision for credit losses for the first
three months of 1998 was $880 thousand, as compared to $682 thousand for the
same period in 1997, an increase of $198 thousand or 29.0%. After net
charge-offs of $328 million and provisions for the first three months of 1998,
the Bank's allowance for credit losses increased by $552 thousand from $7.4
million on December 31, 1997, to $7.9 thousand on March 31, 1998. Please refer
to the earlier discussion of ALLOWANCES FOR CREDIT LOSSES AND NON-PERFORMING
LOANS for additional insight to management's approach and methodology in
estimating the allowance for credit losses.

NON-INTEREST INCOME - Total non-interest income for the three month
period ended March 31, 1998 was $2.6 million, as compared to $2.1 million for
the same period in 1997, an 


                                       11
<PAGE>   12

increase of $508 thousand or 24.1%. The increase is due primarily to growth in
the Bank's deposit base, resulting in increased fee income. Also, the Company
recorded equity earnings of $193 thousand from Sterling Capital Mortgage Company
during the first quarter of 1998, compared to a break-even position for the
first quarter of 1997.

NON-INTEREST EXPENSE - Non-interest expenses increased $2.5 million, or 27.7%,
to $11.6 million for the first three months of 1998 as compared to $9.1 million
for the same period in 1997.

Salaries and employee benefits for the three month period ended March 31, 1998
were $6.2 million, as compared to $5.2 million for the same period in 1997, an
increase of $1.1 million or 20.4%. The increase is due to an increase in the
number of employees. Full time equivalent employees increased by 78, from 392 in
March 1997 to 470 in March 1998 or 19.9%. The increases in headcount were across
the board between the banking offices and the central support divisions and were
a result of supporting a larger customer base. The remaining increase in
personnel costs may be attributed to normal market adjustments and
cost-of-living pay increases.

Technology expense for the three month period ended March 31, 1998, was $734
thousand as compared to $457 thousand for the same period in 1997, an increase
of $277 thousand or 60.6%. The increase is principally due to depreciation
expense relating to the new mainframe computer system installed in April 1997
and an enhanced teller platform installed during September 1997. These new
systems should provide the infrastructure for future expansion.

Minority interest expense represent the interest expense of the subsidiary trust
on the Trust Preferred Securities. These securities were issued during the
second quarter of 1997.

Other non-interest expense was $2.0 million for the three month period ended
March 31, 1998, as compared to $1.8 million for the same period in 1997, an
increase of $209 thousand million or 11.7%.

ITEM 3.  QUALITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK.

There have been no material changes since December 31, 1997. See Form 10K, Item
7 "Management's Discussion and Analysis of Financial Condition and Results of
Operations -- Interest Rate Sensitivity and Liquidity".

PART II. OTHER INFORMATION

ITEM 1.  Not applicable.

ITEM 2.  CHANGES IN SECURITIES

There were no changes in securities during the three months ended March 31,
1998.

ITEM 3.  Not applicable.

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

There were no matters submitted to a vote of security holders during the three
months ended March 31, 1998.



                                       12
<PAGE>   13

ITEM 5.  Not applicable.

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

Exhibits:

      EXHIBIT 11.  COMPUTATION OF EARNINGS PER SHARE

        Included as Note (2) to Interim Consolidated Financial Statements on
        page 5 of this Form 10-Q.

      EXHIBIT 27.  FINANCIAL DATA SCHEDULE

        The required Financial Data Schedules have been included as Exhibits 27
        and 27.1 of the Form 10-Q filed electronically with the Securities and
        Exchange Commission.

SIGNATURES

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

                                       STERLING BANCSHARES, INC.
                                       -------------------------
                                              (Registrant)


                                       BY: /s/ George Martinez
                                           ------------------------------------
                                           GEORGE MARTINEZ
                                           CHAIRMAN AND CHIEF FINANCIAL OFFICER



                                       13
<PAGE>   14
                               INDEX TO EXHIBITS


<TABLE>
<CAPTION>
EXHIBIT
NUMBER                             DESCRIPTION
-------                            -----------
<S>     <C>
  11    COMPUTATION OF EARNINGS PER SHARE

        Included as Note (2) to Interim Consolidated Financial Statements on
        page 5 of this Form 10-Q.

  27    FINANCIAL DATA SCHEDULE

        The required Financial Data Schedules have been included as Exhibits 27
        and 27.1 of the Form 10-Q filed electronically with the Securities and 
        Exchange Commission.
</TABLE>