When Joyce Williams and other parents of handicapped children gather every month at the D.C. Parent & Child Center at 13th and W streets NW, the conversation usually revolves around the sometimes heavy burdens on their families, she said, and the mood ranges from serious to grim.

But that has changed somewhat in the past year since they formed a new group dedicated to a simple yet elusive goal: fun.

"We had only discussed the serious and difficult aspects of our situation," said Williams, a single working mother whose 5-year-old son, Joshua, has Down's syndrome. Now, she said, the talk is often about planning their beach trips, ball games, museum outings, picnics and other forms of recreation that allow tense families to relax.

Yesterday, hundreds of handicapped people and their families from throughout the nation gathered on the Mall for a day of recreation to celebrate the organization's first National Family Day. Let's Play to Grow counts 6,000 families in its 200 clubs. There are five in the District, two in Virginia and one in Maryland.

As a national trend has taken hold in the past decade -- shifting the mentally ill and retarded from institutions into the community -- the families of the nation's estimated 6 million handicapped children are being challenged to find new ways to cope. They must adjust, not just to the handicap, but also to the effect on the other family members.

"So many families refuse to even go out in public. It takes a lot for them to overcome the shame and the fear," said Joann Stevens, a spokesperson for Let's Play to Grow, a small but growing national organization dedicated to breaking down such barriers and liberating families through group recreation.

"The most important moral agent in the community is the family. The most important political force in the country is the family," said Eunice Kennedy Shriver, executive vice president of the Joseph P. Kennedy Jr. Foundation, the group that sponsors the Special Olympics for handicapped children and set up the recreation clubs for their families.

"You are all making a major contribution, and your children are, too . . . . You deserve a great deal of credit," Shriver told them, before joining handicapped youngsters and adults in a volleyball game with a low net and an oversized beach ball. Refereed by ABC-TV reporter Steve Bell, the game ended in a tie, with everyone declared winners.

Handicapped children and their nonhandicapped brothers and sisters came out for ball-playing, face-painting, balloon-blowing, golfing and putting aside their wheelchairs, in some cases, to sit down and play with other smiling youngsters.

The grass roots Let's Play to Grow clubs operate on shoestring budgets and do not charge dues. They make toys and games and raise funds for their activities. For families that have become virtual shut-ins, the outings may be as simple as a dozen families organizing a trip to dinner or a movie.

"It's so important for the brothers and sisters of handicapped kids to meet these other families," said Williams, whose job as a personnel director often leaves her and Joshua little time for socializing.

In club outings, she said, "Kids see that their siblings are not the only handicapped kids around, and they learn to feel better about it."

Devin Reston, 5, of Bethesda, and his sister Maeve, 7, have had problems at times adjusting to the handicap of their little sister, Hillary, who at 22 months began losing her speech and coordination from an undiagnosed neurological ailment, said their mother, Denise Leary.

"They get very upset sometimes, and this is good for them to see that Hillary isn't the only one" who has such problems, said Leary, who said events like yesterday's help her perspective, too.

"Sometimes, you just get so sad, as a parent, and the demands get so big," she said. Leary exchanged information yesterday with other parents about special equipment and programs for the handicapped, and said she would like to join the group.

Karen Ihrig, a Nebraska teacher of handicapped children, started a Let's Play to Grow club in Omaha four years ago that now has 125 families.

"Families build their own support systems. The fathers come in their ties and jackets after work, and they crawl around on the floor and learn to play with their kids, and the other kids," she said. "They just learn to play."