Washington held its third and largest giveaway of government surplus cheese yesterday--18,780 pounds of cheese, distributed to 3,756 of the city's needy. Still, many city residents, after walking to distribution centers under a hot summer sun, had to go away empty handed.

The distribution, organized by the Council of Churches of Greater Washington, began at noon at 14 D.C. churches. But most of the sites ran out of the five-pound boxes of American cheese well before the scheduled 4 p.m. closing time, and some had run out by 1:30 p.m.

While many unemployed middle-aged men and young mothers receiving Aid to Families with Dependent Children payments lined up for the cheese, it was senior citizens living on modest Social Security benefits who were most in evidence.

Dressed in orthopedic shoes and supported by her cane, 66-year-old Anna Hickman walked to First Rising Mount Zion Baptist Church at Sixth and N streets NW from her home around the corner about 2:30 p.m. But it was already too late.

"Well, I'll just have to make do," said Hickman, who receives $40 in food stamps each month and $233 in Social Security benefits, most of which, she said, goes toward her monthly rent payments of $142. "Lucky thing I don't eat but a little."

Susie Butler, 71, whose legs are swollen from diabetes, walked eight blocks from her home to the Lincoln United Methodist Church at 1304 East Capitol St., wearing a sunshade to protect her eyes, which were recently operated on for cataracts. She, too, arrived too late.

Bobby J. Rogers, a 42-year-old man who works part time at the Creative Recycling Thrift Shop on H Street NE, went to four different distribution sites but came away empty handed each time. At his first stop, the Douglas Memorial Methodist Church at 11th and H streets NE, officials told him he did not have proper identification, even though he showed a Department of Human Services ID card.

Rogers, a tall, wiry man with several days' growth of beard and several missing teeth, then hitched a ride with some other people who also wanted cheese, and went to three other sites. But each place had run out before he arrived.

Still, yesterday's giveaway was far more orderly than the first one last January, when the cheese arrived late and thousands of the city's poor waited for hours in the biting cold. In January, there were only six distribution sites. The lines yesterday were much shorter and moved more quickly, as they also did at the second giveaway in April when 17,600 pounds were distributed, according to a spokeswoman for the Council of Churches.

Dressed in T-shirt, sneakers, checked pants and a baseball cap, Albert Louis Dubois, 57, who said he was a laid-off painter, squinted at the hot sun and recalled how numb his feet were last January when he waited in line for three hours at one Northeast church, then was told there was no more cheese.

Yesterday, at Douglas Memorial Methodist Church, he brought along his food stamps receipt, medical assistance pass and Medicaid card to be sure he could prove he qualified for the free cheese.

Like many of the others, when he finally did get his cheese, he was less than effusive. "My primary problem is I need a job," said Dubois, who said he was laid off by the D.C. government three years ago. "I want to work and I can work. I'm a painter. I've been a painter for 35 years . . . . But I guess they'd rather hire young boys than an old man like me."

Yesterday's giveaway will not be the last, as the city has a total of 100,000 pounds of cheese to distribute from the national surplus of 30 million pounds. The date of the next distribution was not announced yesterday.