John E. Flack of Falls Church, an engineer with the General Services Administration, told friends at the Annapolis airport Saturday afternoon that he had to "get home for dinner" and took off in his small plane in marginal weather for Leesburg, according to his family and friends.

Early yesterday his single-engine Beechcraft Sundowner was found shattered in rugged woods about 1,250 feet up Thoroughfare Mountain between Haymarket, and The Plains, Va., according to Federal Aviation Administration spokesmen.

Flack 48, was found dead in the plane at 1.30 a.m. by a search team that had worked its way up the mountain in darkness after being alerted by hikers who had spotted wreckage on Sunday.

The discovery ended a search that began after Flack's son-in-law, called by Mrs. Flack's wife when her husband failed to return to his Falls Church home, found his car with its windows open at the Leesburg airport. His plane was missing.

Seven Civil Air Patrol planes, two helicopters and 16 ground teams, hampered by bad weather, had searched for Flack on Sunday.

An FAA spokesman described conditions at the time of Flack's takeoff at 5 p.m. Saturday as "marginal." Visibility was at the three-mile minimum and there were rain showers, fog and haze in the area. There were also reports of a line of thunderstorms.

The FAA spokesman said the Flack, who had been flying for 15 years, apparently crashed about 30 minutes after leaving Annapolis on the 54-mile flight. The Leesburg airfield is at an elevation of 388 feet, nearly 900 feet below the crash site 20 miles to the southwest, according to the FAA.

Flack's wife, Nancy, said federal investigators had raised the possibility that Flack might have had a heart attack in flight. She said she was told the plane was flying straight ahead when it hit and that there was no sign of mechanical problems on the well-instrumented aircraft.

Jack Liscomb, air safely investigator for the National Transportation Safety Board, said after returning from the crash site that weather or a physical problem could have been involved in the crash but that at this point in his investigation "it is all speculation. I don't have any answers yet." He said that an autopsy is routine in fatal crashes. A determination of the cause of the crash will take more than a month, he said.

According to NTSB and FAA records for 1976, the last year available, there were 97 crashes in Virginia, Maryland and the District, in which 32 persons died. An NTSB spokesman said that about half of all light-plane crashes are weather related. There are about 2,300 light plans registered in the Washington area, an FAA spokesman said.

Nancy Flack said that her husband flew "at least every weekend" and that his "true love was flying." The Flacks had just completed a new home in Great Falls to which they planned to move this month.

Flack was born in Kansas City, Mo., and was a graduate of the University of Kansas. He had worked for GSA for 13 years and was a specialist in quality control of hand tools. He had served in the Army in Korea and was a member of St. James Catholic Church of Falls Church.

Other survivors include a daughter, Anita Gelles of Herndon; a son, Karl, 18, and a daughter, Laura, 17, of the home; his mother, Lena Flack of Kansas City, and several brothers and sisters.

The family suggests that expressions of sympathy be in the form of contribution to St. James Church or the Civil Air Patrol.