President Reagan returned to Washington yesterday from a three-day trip to Texas aboard the so-called "doomsday" plane--a modified Boeing 747B jet transport that would serve as the national airborne command center in case of a nuclear war.

Presidential counselor Edwin Meese III flew down to San Antonio, Tex. late Saturday to join Reagan, White House chief of staff James A. Baker III and deputy chief of staff Michael K. Deaver on the demonstration flight back to the capital.

The "doomsday" exercise also gave Reagan and his three top aides a chance to huddle after a week of politically damaging revelations involving the president's budget director, David A. Stockman, and his national security adviser, Richard V. Allen. However, Reagan spent much of the flight back to Washington working alone in a forward cabin.

Stockman was quoted at length in the latest issue of Atlantic Monthly as raising serious doubts about the effectiveness of Reagan's economic policies. Allen, meanwhile, is under investigation by the Justice Department for the receipt of $1,000 last January from Japanese journalists who were granted an interview with Reagan's wife, Nancy.

Larry Speakes, Reagan's deputy press secretary, said yesterday he doubted the president's own credibility had been damaged by the Stockman and Allen incidents.

"I know the president hasn't lost any credibility ," Speakes said in San Antonio. "I don't think anybody has any doubts about the president."

Speakes added that Reagan has been "as successful as any president in history" in getting through his legislative program, and expects the president to continue to do well on Capitol Hill.

"We're in very good shape," Speakes said.

Reagan, dressed in blue jeans, a plaid shirt and cowboy boots, boarded the huge, $117 million airborne command plane around 3:15 p.m. EST at the Kelly Air Force Base in San Antonio.

The aircraft, about three-fourths the length of a football field, contains six areas for planning and directing military action in time of national emergency.

The plane can stay aloft for 72 hours without refueling. Lt. Gen. Phillip Gast, director of operations for the Joint Chiefs of Staff, and Col. James Kidd, chief of the National Emergency Airborne Command Post, led the tour and briefing for the presidential party.

Reagan is the second president to have flown aboard an emergency aerial command post. Jimmy Carter used a prototype of the aircraft for his first trip home to Plains, Ga., after he took office in 1977. However, Reagan flew in a newer, more sophisticated model.