The National Park Service's program of free summer concerts, a Washington tradition since 1967, will continue this year thanks to major last-minute corporate sponsorship.

There had been speculation of major curtailments due to government-wide budgetary cutbacks; until last year, all production costs had been borne by the Park Service.

"We've had to look to corporate or private support," said Al Dale, Park Service spokesman. "We need it to keep these things alive. We're finding that arts organizations are all going to the same barn to get the same eggs. What gave us an edge was that we had established successful programs that attracted a large number of people."

The R.J. Reynolds Tobacco Co., the only corporate sponsor in 1981, will once again support the Fort Dupont Theatre weekend jazz series, which last year drew more than 400,000 people. This year, Reynolds will cosponsor the Fort Dupont series with the Anheuser Busch Brewing Co.

Busch will independently sponsor a summer series at the Carter Barron Amphitheatre (which drew 50,000 people last year), while the Performance Trust Fund/Local 1617 will sponsor Monday night big-band concerts at the Sylvan Theatre on the grounds of the Washington Monument.

One casualty, though, is the Shakespeare festival, which will not be held at the Sylvan this year. "That's why we put the big bands in, to have something that would serve that age group, despite the limited funding," Dale explained.

The 4th of July concert on the Mall, which has featured the Beach Boys and huge crowds for the last two years, apparently will be more low-key this year. After Park Service negotiations with Kenny Rogers, the Oak Ridge Boys and several other major groups fell through, radio station WRQX-FM (Q107) stepped in to provide the headline act, which one well-placed source indicated would be the newly reunited Young Rascals. Also on the afternoon show, held before the annual fireworks display: the Tops in Blue, an Air Force show drawing winners from talent shows held on Air Force bases last year.

The Fort Dupont series, running Fridays and Saturdays, begins next weekend with Della Resse and the Blackbyrds. Subsequent shows: Esther Satterfield and Paquito D'Rivera (July 9 & 10); Stanley Turrentine and the local comedy group Huh! (July 16 & 17); a Swamp Jam with Dr. John, Hank Crawford, and Fathead Newman and the Rosella Clemons Quartet (July 23 & 24); Les McCann and the LaVerne Reed Dancers (July 30 & 31); Wynton Marsalis and the Buck Hill Quartet (August 6 & 7); the James Moody and Lou Donaldson Quartets (Aug. 13 & 14); Roy Ayers and the DC Percussion Society (Aug. 20 & 21); and Rodney Franklin and the Lettumplay Jazz Ensemble (Aug. 27 & 28).

The Carter Barron series, for which free tickets are available at Woodward & Lothrop, also begins next weekend, with a Saturday concert by jazz flautist Herbie Mann and, on Sunday, the finals of the D.C. Metro Talent Search. Other major concerts, some of them cosponsored by local radio stations, are scheduled to include: Edwin Birdsong, Waldo, Stanley Woodruff and Deuces (July 9); Red Hot, AM/FM, Kemistry and Noble Jolley (July 23); the Nighthawks and the Legendary Blues Band (July 24); the Dells, Keith Killgo and Crosswind (July 31); Gayle Adams, Janet Rice, Premiere International and Sass (Aug. 6); Ray Goodman and Brown (Aug. 7); a gospel program with the Dixie Humminbirds, Inez Andrews and the Tabernacle Echos (Aug. 8); Angela Bofill with Jon Carroll and Metro (Aug. 14); the Manhattans (Aug. 15); Noel Pointer and Juan Valentin (Aug. 21); Laverne Reed Dancers and the Ambassadors (Aug. 22); an oldies night with Jr. Walker and Martha Reeves (Aug. 28); and the Nat Adderley Quintet and Come Out Swinging (Aug. 29).

Several classical programs are scheduled for Carter Barron, as well, including a D.C. Youth Orchestra series featuring special guest performers (Ruth Laredo, July 11; Eugene Fodor, July 18; Sharon Robinson, July 25; and Billy Taylor, Aug. 1); a production of Gilbert and Sullivan's "The Mikado" by the Washington Savoyards (July 16 & 17); and three family nights (July 30, Aug. 13 and 20) with jugglers, clowns and musical entertainment, sponsored by McDonald's restaurants.

Finally, the big-band shows at the Sylvan, which began Monday with the Trux Baldwin band, will feature a concert in the first half of each show and dance music in the second half. The schedule, with some bands yet to be announced, runs through the end of August and includes Doc Dikeman (June 21), Fred Perrantoni (July 12), Gene Donati (July 19), William Gray (July 26), Tony Kelly (August 9) and Howard Devron (August 16).