For the past two years, it has been called the Mayor's Cup. This year, it is being called the Mayor Marion Barry Invitational. Under any name, it is one of the best amateur boxing tournaments in the Washington area.

"It's more than just a boxing tournament," said Rick Bowlding, director of the tournament being held tonight, Wednesday, Friday and Saturday at Howard University's Burr Gymnasium, starting at 7:30 each night. "It's a whole package. A happening, you might say."

Athletes from 12 teams (Washington; New York; Atlanta; Detroit; Philadelphia; Miami; Norfolk; Elmira, N.Y.; Charleston, S.C.; Jersey City, N.J.; Fort Bragg/Camp Lejeune, N.C. and the Navy) will be here to box in each of the 12 amateur weight classes. Each team features its area's top competitors, including some who may participate in the Olympic Festival or the Pan American Games.

However, these athletes also will participate in a series of nonboxing activities from seminars about substance abuse and self-esteem to a black history tour of Washington to visits with Congressional representatives. Sunday there will be an awards breakfast with former world heavyweight champion Floyd Patterson as the keynote speaker.

"With all that Washington has to offer," Bowlding said, "it would be kind of senseless to bring these kids in from all around the country and then restrict their activities to just boxing."

The tournament, which began as a way for the Washington area to showcase its amateur boxing talent (four 1985 national champions were from the District), first involved eight teams. Last year, it was increased to 12. In the future, Bowlding hopes to make this a truly national tournament, with teams representing each of the U.S. Amateur Boxing Federation's 18 regions.

For now, the main attraction is the two-time defending champion Washington team, coached this year by Larry Williams of the Washington Highlands Community Center and John Sneed of D.C. Police Boys and Girls Club No. 11. Washington, which over the past two years has won 11 of a possible 14 titles in the seven lowest weight classes, is led by 106-pound James Harris, 125-pound Tyrone Washington, 132-pound Frank Payne, 147-pound Gary Payne and light heavyweight Michael Simon. Harris and Frank Payne are two-time champions in this event.

Tickets for the tournament are $3 for each night and will be available at the door.