The Justice Department has sued Youngstown Steel Corp. and its chief officers and stockholders for more than $17.5 million in damages, charging that the firm falsified a $10 million loan application to the Commerce Department's Economic Development Administration.

Individuals named as defendants include Charles J. Lang of Sewickley, Pa., president of the board in May 1980, when the Justice Department says the incident occurred; Andrew K. Wood of Osborne, Pa., who is president, a director and a stockholder of Youngstown; and Ronald J. Garmey of Pittsburgh, vice president, assistant secretary, a director and a stockholder in the corporation.

Youngstown applied for the loan to build a modern, operational steel mill on the site of the old Youngstown Sheet and Tube Co. in Struthers, Ohio. The EDA, which helps businesses in economically distressed areas, approved the loan.

The government paid $8.75 million before discovering that Youngstown never opened the steel mill. The Justice Department said yesterday that the company has paid back none of the loan, which went into default last February.

The lawsuit is being handled by the civil division under the False Claims Act, which gives the government the right to sue any person who knowingly submits a claim containing false or fraudulent statements.