U.S.-Egyptian exercises designed as the first big test for the Carter administration's Rapid Deployment Force in harsh Middle East conditions got off to a tragic start with the crash here of a C141 transport jet that killed 13 Americans.

The plane, which was delivering equipment to U.S. forces bivouacked on the sands west of the Egyptian capital, crashed just before midnight last night on approach for landing in clear weather at the Cairo West Air Base maintained by the Egyptian Air Force.

Wreckage from the giant craft littered more than a half a square mile of the flat, almost windless, desert about nine miles northeast of Cairo West, which lies 25 miles west of the city. Military police preventing anyone from approaching the scene told correspondents that the operation commander, Marine Lt. Gen. Paul X. Kelly, was among U.S. and Egyptian officials on the spot trying to find out why the crash occurred.

[Pentagon officials in Washington said the plane was carrying explosives, liquid oxygen equipment, trucks and spare parts but that it was not known what caused the crash. The victims included 11 men and two women, they said, making up a flight crew and cargo handlers for the transport plane attached to the 62nd Airlift Wing based at McChord Air Force Base near Tacoma, Wash. Their bodies were quickly flown to West Germany and from there to Dover Air Force base, Del., they added.]

It was the second fatal air mishap since mid-August involving American pilots in joint exercises with the Egyptians at the heavily secured Cairo West base. An F4E Phantom fighter-bomber at the time plowed into the desert south of the strip during operation Proud Phantom, an earlier U.S.-Egyptian exercise aimed at facilitating American use of Egyptian air bases in case of a Persian Gulf crisis.

The Phantom, too, had been making its last approach. Both Americans at the controls were killed. The cause of that crash is still unknown.

The current long-range deployment exercise, Operation Bright Star, is bringing 1,400 U.S. ground and air forces to Egypt's hot, windy deserts. This is believed to be the first time such a large number of American fighting units has been assigned here since World War II.

Their proclaimed aim is to practice under conditions that would be similar to what might be found southeast of here in the Persian Gulf. President Carter has promised the United States will use force if it is needed to defend gulf tanker routes menaced by the Iranian-Iraq war and, some strategists fear, by Soviet presence in Afghanistan.

Operation Bright Star, the cost of which has not been reported by the Pentagon, is scheduled to last for two weeks, highlighted by day-and-night maneuvers, including some with live ammunition. Egyptian officials said its schedule will not be altered because of the crash.

"The Americans will gain experience in the terrain and the weather," said Gen. Mohsen Hamdi, an Egyptian Army spokesman.

He reminded reporters at a news conference that Egypt has offered Washington temporary "use" of Egyptian bases in order to come to the aid of a threatened Middle East nation but will not grant extraterritorial base rights similar to those held by the United States in Europe.

The Egyptians are sensitive to American military activity on their soil. Nothing about the deployment forces appeared in today's newspapers, and only a squib appeared yesterday. That was an American dispatch reporting the first of the units had departed from the United States.

Even after the two Americans died in the Phantom crash in August, the Egyptian military refused to permit Western, or even Egyptian, reporters onto Cairo West for the memorial ceremonies honoring the dead pilots.

The Egyptians recall too well, perhaps, the days when Soviet military advisers dominated Egypt's armed forces and Egyptian pilots needed Russian-authorized passes to get onto their own base at Cairo West.