Federal investigators said tonight that one engine of the Midwest Express jetliner that crashed here Friday afternoon was not working when the plane hit the ground, killing all 31 people on board.

However, investigators said, the apparent engine failure does not account for the plane rolling out of control and diving almost nose first into the ground, because twin-engine McDonnell Douglas DC9 planes such as this one are designed to fly safely on one engine.

Several parts of the same kind of airplane engine have been recovered along the runway used by Flight 105, scheduled to travel from Milwaukee to Atlanta. However, National Transportation Safety Board Chairman Jim Burnett said, it has not been determined if those parts belong to the engine that was not working.

Furthermore, those parts were located on the left side of the runway. The engine that failed was on the right side of the plane and the plane came to ground somewhat to the right of the runway's center line extended. The left engine was apparently functioning when the plane crashed, Burnett said.

A logical explanation of the engine failure would be that a errant part severed some vital control system, but Burnett said there is too little evidence to draw that conclusion.

Impact with the ground so severely damaged vital controls, cables and hydraulic systems in the rear of the plane, that "identification of control surfaces may be beyond us," Burnett said.

The JT8D engines were manufactured by Pratt & Whitney, a division of United Technologies, Corp. However, the model of JT8D on this airplane is different from the JT8D engines involved in six recent incidents in which a major engine part has broken loose. It is also a different model from the JT8D apparently involved in the British Airtours accident in Manchester, England, on Aug. 22, in which 54 people died.

Nonetheless, investigators are concerned about problems with the world's most widely used jet engine. Various models of the JT8D power two-thirds of the U.S. domestic jet fleet.

Investigators hope to extricate the right engine from the wreckage as soon as possible and examine it completely. There is no visible evidence that any major piece of the engine is missing, but the bottom half of the engine cannot be viewed, because it is buried in the ground.

A DC9 pilot for a major airline interviewed today said, "I have been though an engine failure just 800 to 1,000 feet off the ground, and the airplane is definitely flyable. Something else had to have happened."

Burnett said tonight the highest altitude the plane reached was 900 feet above the ground.

There is no evidence of a bomb, Burnett said.

According to witnesses, the plane rolled to one side or all the way around before diving. One of the plane's crew members radioed, "We have an emergency here," but he had no time to explain it.

The wreckage is contained within an unusually small area for a commercial plane crash, perhaps no more than 100 yards square. A deep gouge in the ground marks the point of contact. Both engines, the landing gear and one wing section are the only readily identifiable parts of the plane.

All of the bodies have been removed from the wreckage and taken to a temporary morgue by Milwaukee County officials.

The plane also killed a deer as a crashed into a stand of trees just south of the airport. Perhaps 50 trees stand like charred matchstickes set up in a row. Canisters of firefighting foam litter the wreckage but do not eliminate the stench of burned kerosene, plastic and aluminum.

The plane's two "black boxes" suffered severe batterings and fire damage, but Burnett said the cockpit voice recorder has a useable tape and some data can be retrieved from the flight recorder.

Midwest Express has been a scheduled airline since June 1984. It is owned by Kimberly-Clark Corp., the manufacturer of Kleenex and other paper products.