After 56 years in the menswear business, Baltimore-based Webster Clothes Inc. announced yesterday it has agreed to be acquired by a national retailing giant in a cash transaction valued at $19.2 million.

The sale to Edison Brothers Stores Inc. ends a turbulent period for family-run Webster's, whose 128-store upscale clothing chain suffered through its second year of losses last year. The downturn stems primarily from costly expansion plans that backfired and sent the stock tumbling from a high of about $4 in 1987 to $2 recently.

St. Louis-based Edison Brothers made a cash tender offer of $6 for Webster's 3.2 million outstanding shares, a bid that boosted its stock up to $5 in over-the-counter trading yesterday. The Midwestern retailer is a leader in the men's clothing business, with 1989 sales of $919 million and more than 2,500 stores.

Edison, whose stores include Oak Tree, 5-7-9 and the Baker and Wild Pair shoe chains, is expected to pay for the deal through cash raised in a $86 million June stock offering, analysts said. Webster operations will continue under its own name as a subsidiary in St. Louis, said Edison Chairman Andrew Newman.

"Edison has a proven and successful track record in operating its apparel stores," said Webster chairman and principal shareholder Samuel M. Feldman in a prepared statement.

The company declined to comment further until the deal is closed, probably next month.

"This appears to be one of those acquisitions where it's good for both the buyer and the seller," said Steve Schneider, research analyst with Stifel Nicolaus & Co. Several analysts cited Edison's previous successful acquisitions and turnarounds of failing retailers, most notably menswear retailer J. Riggings in 1987.

Feldman, who is the son of the company founder, controls more than 60 percent of Webster stock by himself and through relatives, while other officers and an outside investor own another 21.8 percent.

The companies said Edison has obtained an option from Webster shareholders to purchase about 81 percent of the stock.