ROCK ISLAND, Ill. (AP) _ Augustana middle guard Brian King relishes the day a few years from now when he is asked about his college football team.

''When people ask us, 'How did your college do?,' they'll think we're joking,'' King said. His team went unbeaten for four years and won its fourth consecutive NCAA Division III national championship Saturday with a 31-3 victory over Salisbury State of Maryland.

''It's awesome winning four national championships,'' said running back Brad Price, who capped a 1,000-yard rushing season by running for 162 yards and three touchdowns in the title game, also known as the Amos Alonzo Stagg Bowl, at Phenix City, Ala. ''We seniors can say we never lost a game.''

And that unbeaten streak for King, Price and 10 other seniors on the traveling team goes back 50 games.

The Vikings' only non-victory in four years was a 0-0 tie at Elmhurst College at the beginning of the recently-completed season. The Vikes started their streak in 1983 with a 42-14 season-opening win over Carroll after losing the 1982 Stagg Bowl to West Georgia 14-0.

''It almost seems metaphysical,'' said senior defensive tackle Lynn Thomsen, the only player to start all 50 Augustana wins. ''It's hard for me to realize that being part of history is something that happens, if you're lucky, once in your life.''

Tom Billups, a senior reserve linesman, said, ''To be able to play four years at this level and never taste defeat, that's really something. They'll never be able to take this away from us.''

Only about 100 people or so greeted the team at the Quad Cities Airport on their flight home from Alabama on Saturday night, but many more attended campus celebrations, including one at the house King shares with two other players.

''It was wall to wall. People never stopped coming in,'' King, a 6-foot, 225-pounder from Crystal Lake, said in a telephone interview Monday. ''We went through a few kegs of beer.''

The Vikings go for beer parties and no-frills football.

Augustana wins with a rushing game off a wishbone offense and a very solid defense. The Vikings threw only 73 passes all season in 13 games.

''No one saw anything they haven't seen the last four years,'' Vikings Coach Bob Reade said after Saturday's game. ''The secret here is to play your game and to play it well.''

The Vikes have played very well game after game. They led the nation defensively this year, giving up an average of under 25 yards rushing and fewer than six points each game, while the offense generated a total of 446 points.

Reade, 54, is 81-8-1 at Augustana and ranks No. 1 for winning percentage among all active NCAA football coaches with more than five years experience. He reportedly unsuccessfully applied for the Iowa State head coaching job.

''Reade is a quiet coach. He never screams, but he gets his point across,'' said King. ''His only rules are: Obey law and be a gentleman.''

Everybody wonders how Elmhurst, a 2-6-1 team, managed to tie mighty Augustana, but King explained, ''We had a young offensive line and couldn't get rolling. We were at our worst and Elmhurst was at its best.''

With an enrollment of 2,200, Augustana is a liberal arts college affiliated with the Lutheran Church of America.

Rock Island is 160 miles west of Chicago, with Iowa just across the Mississippi River, but 98 percent of Reade's team is from Illinois and 80 percent are from the Chicago area.

After Augustana, football is over for Reade's players, the pros do not beckon them. At least, that has been the case in the past.

Kurt Kapischke - a 6-5, 260-pound offensive tackle from the 1983 title team - was cut in practice by the Michigan Panthers of U.S. Football League and released as well as by the Dallas Cowboys and Green Bay Packers of the National Football League. Lance Hofer, who quarterbacked the 1982 Vikings, was cut in practice by the Hamilton Tigercats of the Canadian Football League.

King, who majors in math and public administration, said he feels a little sad that the winning is over for him.

''It a great feeling to go through your college career undefeated,'' he said, ''but next fall when football starts up again, I'll be a spectator.''