PITTSBURGH (AP) _ Mellon Bank Corp., one of the nation's biggest bank holding companies, says it will lay off an unspecified number of employees because of sinking profits and rising expenses.

Mellon, the nation's 12th largest banking concern with assets of $34.5 billion, is Pittsburgh's third-largest private employer with 8,000 workres in the metropolitan area.

It had more than 18,000 employees at all locations last year.

Due largely to troubled loans overseas and in the oil industry, Mellon's profit fell by 9.1 percent last year to $183.3 million, including a 65 percent drop in fourth quarter net income.

The employee cutbacks had been rumored since December when Chairman J. David Barnes began sending employees letters about a need to develop a ''productivity culture.''

Bank officials expect to review payrolls at headquarters and all of Mellon's outlying locations. The company said the reviews still are taking place and did not indicate when they might be completed.

''Each business unit of the corporation has been asked to manage its operations in a way that meets corporae productivity goals while keeping in mind business objectives,'' Mellon said in a prepared statement. ''Some units will do so by means of a cut in personnel.''