Murry's Steaks Inc., a Washington-area family-owned food business for 38 years, was sold yesterday for $60 million to Rymer Co., a restuarant and food-service supplier from suburban Chicago.

Rymer will pay $44 million in cash, $16 million in notes and a percentage of future earnings to members of the family of Alfred G. Mendelson, who founded the company in 1948 and named it for his son Murry.

Murry Mendelson, now chairman of the board, has negotiated a six-year contract to work for Rymer. His son, Ira Mendelson, the company president, said his father decided to sell out in order to diversify the family's financial holdings as well as to be part of a public company.

Murry's had sales of $146 million in fiscal 1985 through its 114 retail stores in the District and six mid-Atlantic states and other outlets. The management and 1,400 employes will remain with the company, which will continue to operate from its headquarters is Forestville, Md.

Murry's specializes in moderately priced, portion-controlled meat, seafood and poultry. In addition to the company-owned retail stores, Murry's sells its products to about 5,000 wholesale customers such as hotels, schools and military commissaries. It also owns a downtown Washington restaurant named New York, New York and is constructing two others in the region. About 40 percent of Murry's sales come from products processed at its Lebanon, Pa., production facility.

"Murry's outstanding record and the expansion potential of their retail store operations were the prime reasons for this acquisition," said Michael J. Burns, Rymer's president. "Murry's complements our present portion-controlled food-processing business, which currently serves family restaurant chains."

Rymer plans a major expansion of Murry's, starting with 30 additional Murry's stores in the next year. Murry's will move into the NewYork market by opening a store in Brooklyn later this month and plans "a whole cluster of stores in the New York area," a spokesman said.

Rymer, located in Rolling Meadows, Ill., had sales of $92 million in fiscal 1984 and net earnings of $6.5 million, including a one-time $3.2 million tax-loss carry-forward. Rymer stock closed unchanged at 15 on the New York Stock Exchange yesterday.

Like Murry's, Rymer buys sides of beef from meat packers and processes them into meal-sized, ready-to-cook portions for restaurants and other customers. Rymer's principal business is serving family restaurants; its products include steaks for chains such as Bonanza, and marinated and flavored meats for Mexican and Japanese restaurants.

Alfred Mendelson, when he owned a small grocery store, hand-formed his first two-ounce steaks using a wooden mold, launching a company that became one of the largest retail specialists in portion-controlled food.

In addition to meats, Murry's also sells frozen convenience foods and other nonperishable items in institutional-size packages.