Navy halfback Eddie Meyers, who wasn't drafted by any National Football League team because he has five years to serve with the Marine Corps, has signed with the Atlanta Falcons as a free agent, it was announced yesterday.

Meyers, who was commissioned a second lieutenant when he graduated from the Naval Academy in May, signed a two-year contract with the Falcons three weeks ago. He hopes to follow the example of Navy Heisman Trophy winner Roger Staubach, who fulfilled his military obligation before joining the Dallas Cowboys.

The 23-year-old Meyers, whose rushing average of 131.8 yards was fifth in the nation last year, will spend most of his 30 days of annual leave for the next several years training with the Falcons.

"It's going to be a tough experience trying to make it after five years," said Meyers. "I'm going to have to maintain myself mentally and physically. And some tennis and basketball and volleyball once in a while isn't going to do it."

Meyers said he plans to do everything from constant running on base to wrestling on the Marine team to keep in shape and maintain his competitive edge.

"The mental part with me will probably be the biggest thing, just keeping from getting gun shy," Meyers said.

"But as far as ability goes, I think I'll be hitting my prime by the time I'm out. Eighty percent of the rookies in the NFL sit on the bench for an average of two to three years, anyway--even the first-round picks--so I don't think I'll be that bad off.

"When I started at the academy, I was just hoping to make the team, and then when I made the team, I was just hoping to play. Everything fell into place by my junior year, and then I started to think about maybe playing pro ball."

Meyers gained a school-record 1,318 yards last year and was named most valuable player in the Liberty Bowl. His 2,935 yards in four years was also a school mark.

The Falcons originally wanted to draft him in the first or second round, Meyers said, until they realized he would have the military obligation.