Gliding on a cushion of hot desert air, a string of giant U.S. Air Force C5A Galaxies and C141 Starlifters began flying into Cairo West Air Base today to launch the biggest overseas exercise ever held by the U.S. Rapid Deployment Force.

As the transports landed amid the sand dunes that surround the Soviet-built complex northwest of here, battle-dressed troops flown from the United States quickly poured out. Then the planes refueled and took off again for a return trip to pick up more U.S. soldiers in what is to be a three-day airlift for an ambitious multinational Middle East training exercise code-named Operation Bright Star '82.

By the time the airlift is completed late Wednesday, the United States will have deployed about 4,000 troops in a tent city in the desert for a series of airborne and armor exercises with Egyptian forces that, among other things, will feature bombing runs by B52s flying nonstop out of Minot Air Force Base in North Dakota.

The joint U.S.-Egyptian part of the maneuvers is to involve a tactical fighter squadron of A10s from the 353rd Tactical Fighter Squadron at Myrtle Beach, S.C., and two full battalion task forces: one from the 82nd Airborne Division out of Ft. Bragg, N.C., and the second from the 24th Mechanized Infantry Division from Fort Stewart, Ga. They coincide with other, smaller U.S. military exercises in Somalia, the Sudan and Oman at the mouth of the Persian Gulf.

Commanded by Lt. Gen. Robert C. Kingson, the chief of the Rapid Deployment Force, Bright Star '82 is the most ambitious U.S. demonstration yet of its ability to deploy the 1 1/2-year-old strike force in the volatile Middle East area.

Military officials here have been quick to insist that the exercise had been planned in its exact form months ago despite earlier reports, including statements by Secretary of State Alexander M. Haig Jr., that it had been expanded because of the assassination of president Anwar Sadat of Egypt last month.

Nevertheless, this year's deployment clearly dwarfs the exercise held in Egypt a year ago. At that time, the exercises were confined to Egypt, they involved only 1,400 U.S. troops, minimal field equipment and few battle-trained officers.

That exercise was a disappointment to Egyptian military officers, who had hoped to have the opportunity to exchange experiences and tactics with veteran U.S. battlefield commanders and study the newest U.S. field weaponry. Egyptian military leaders expressed their disappointment at the time to their U.S. counterparts, prompting this year's exercises to be expanded in size and scope even before Sadat's death Oct. 6.

The first units arriving at Cairo West today were from the 24th Mechanized Infantry Division and will be linking up Tuesday with their complement of M60 tanks and M113 armored personnel carriers when the vehicles arrive by sea at Alexandria aboard a German-chartered "roll-on, roll-off" (RORO) ship that picked up the heavy field equipment last month at Savannah, Ga.

The infantry units will be followed by the 82nd Airborne units who will get the exercises under way Saturday with a parachute drop in Egypt's vast western desert with the backing of tactical air support provided by both Egyptian and U.S. air forces.

The airborne exercise will be followed by a week's training period involving the U.S. and Egyptian forces, including discussion on tactics and instruction in the use of the U.S. weaponry being deployed for the maneuvers.

The exercise will end with a three-day operation involving all the 4,000 Americans and a like number of Egyptian troops who will simulate the taking of an objective in the desert, defending it and turning it over to another unit. It is during that exercise that a squadron of B52s, believed to number about eight, will make a run with live bombs after a direct flight, with in-air refueling, from their base in North Dakota.

The exercises elsewhere in the region will be minor by comparison. In the Sudan, a unit of 350 U.S. Special Forces hold training exercises in counterinsurgency tactics with the Sudanese Army. In Somalia, noncombatant U.S. engineering and medical units will train at the former Soviet naval and airbase at Berbera while Somali soldiers observe the operation. And in Oman, more than 1,000 U.S. Marines at sea with the U.S. Indian Ocean Fleet will stage a small, one-day amphibious landing near the southern city of Salalah, the capital of Dhofar Province bordering Marxist-ruled South Yemen.