Without horse-drawn caisson or elaborate tombstone, Francis R. (Dick) Scobee, the commander of the space shuttle Challenger, was buried on his birthday yesterday in a service at Arlington National Cemetery as low-key as his life.

Scobee's wife, June, knelt and placed a red rose against the simple tombstone, just paces from the graves of three servicemen who died trying to rescue the American hostages in Iran.

Scobee, a retired Air Force officer who would have been 47 yesterday, was buried with military honors three months and 22 days after Challenger exploded, killing its crew of seven. His midmorning funeral, under a crystal-blue sky, came two weeks after services at Arlington for Challenger pilot Michael J. Smith, the space shuttle's second-in-command.

Teacher Christa McAuliffe and Ronald E. McNair also were buried earlier this month, and the ashes of Gregory B. Jarvis were scattered over the Pacific Ocean. Ellison S. Onizuka will be buried in the next few weeks in his home state of Hawaii. Judith A. Resnik's family has not announced any burial plans.

More than a hundred friends, relatives and colleagues, arranged in a wide semicircle around the grave, attended the 18-minute ceremony for Scobee, a former airplane mechanic from Cle Elum, Wash., who worked his way into an officers' training program and pilot school.

The ceremony followed a private chapel service in which "The Impossible Dream" and "High Flight" were sung, and Scobee was eulogized by astronaut Norm Thagart.

At the graveside, a bouquet of brilliant yellow roses from his fellow astronauts and a wreath of carnations and lilacs from President and Mrs. Reagan adorned the tomb, into which Scobee's remains had been placed early yesterday morning before the service.

The tombstone, on which was etched the wings of an Air Force astronaut, also will bear the epitaph: "A modest man, a faithful friend, a private man who loved his family dearly and contributed mightily to his country's air and space effort." Although the tombstone listed his rank as lieutenant colonel, the Air Force said its records listed him one rank lower as a retired major.

A soft breeze blew in the morning's gathering heat as the U.S. Air Force Band from Bolling Air Force Base played hymns and June Scobee clasped the hands of her children, Kathie Scobee Krause and Richard Scobee, their fingers intertwined.

After a brief sermon, inaudible to many because of the roar of jets at nearby National Airport, a seven-man Air Force honor guard fired three volleys, and a lone bugler under a tree on the hillside played a warbling taps.

Scobee, a down-to-earth, hard-working man who was uniformly well liked by those with whom he worked, was an anomaly in the astronaut corps. Chosen by the National Aeronautics and Space Administration close to his 40th birthday, he was one of the oldest men to become an astronaut, and one of the few to have started his career as an enlisted man.

Except for the attention heaped on him by the media and the public, Scobee loved his job, and accepted its risks. "When you find something you really like to do and you're willing to risk the consequences of that," he once said, "you really probably ought to go do it."