Continental Illinois Corp., the troubled bank company that was rescued by the federal government last summer, formally announced yesterday that 10 of its 14 nonmanagement directors have been forced out by the Federal Deposit Insurance Corp.

Nine of them will serve until the next Continental shareholders meeting in April and another will resign Dec. 17.

The FDIC purge of Continental directors is seen not only as a punishment for them, but as a warning to directors elsewhere that they must scrutinize more carefully the management of bank companies on whose boards they serve.

The FDIC required that directors elected to the board before 1980 not stand for reelection in April. FDIC sources said that FDIC Chairman William M. Isaac believes those directors approved and supervised the rapid growth strategy that got the giant bank into trouble.

Continental's fortunes began to decline in July 1982 when it was disclosed that the bank bought more than $1 billion in bad energy loans from Penn Square National Bank in Oklahoma City. The bank's loan portfolio continued to deteriorate and the bank experienced a severe run on its deposits in May.

The FDIC had to inject $4.5 billion into Continental to save it.

The FDIC said last summer that it was contemplating board changes, but former Standard Oil of Indiana chairman John Swearingen, whom the FDIC brought in to run the institution, argued unsuccessfully against the wholesale changes.

Among those forced to resign were Robert H. Malott, chairman of FMC Corp.; James F. Bere, chairman of Borg-Warner Corp., and Paul J. Rizzo, vice chairman of International Business Machines Corp.