Diane Loretta Smith's life in recent years has been a series of moves, of sleeping secretly on one relative's couch for a while and then moving in with another, hoping she will not get a sister of aunt in the trouble because of overcrowding while she searches for an apartment large enough that a 25-year-old woman on public assistance with three children can afford.

Smith's plight is a familiar one to hundreds - perhaps thousands - of people in the Washington metropolitan area living on fixed incomes. Her attempts to find housing have been met most often with closed doors, and her inability to find an apartment has led to other problems.

Smith and her children now are living temporarily in a Northwest Washington apartment, shared with a sister and her children and a friend - 12 people in a three-bedroom apartment altogether. Before that, she and her children were staying at a one-bed-room apartment with another sister. There were seven people in that apartment. It is a way of living called "stretching out," Smith said.

Smith, a dark, chocolate brown woman with a closely cropped Afro has been on the waiting list for public housing since 1974. This year, she tried to apply for a federal rental subsidy program through the D.C. housing department, but was told the department was not accepting any more applications.

Smith, with Attorney Roy Kaufmann's help, has sought private housing. Most landlords ask that a tenant earn in a week the monthly rent of the apartment however. That disqualifies her for most places because she gets only $314 a month in public assistance payments, and $77 of that amount goes for food stamps for her family.

She is trying to continue her education by taking retail, fashion and typing classes at the Lacaze-Gardner school and currently has no job. That usually means she is ushered quickly out the door of rental offices. When "I tell them I'm not working and am on public assistance, . . . man, I'm on my way out of the door," Smith said.

At first, she could not get her children enrolled in a day care center because she had no permanent address. She was afraid that if she used her sister's address, the landlord would find out she is staying there and force her to move. In desperation, she said, she used the address, anyway.

The housing crisis in the area is creating a "difficult almost impossible" situation for many D.C. residents, said Valerie Moyo, a social worker with the D.C. Department of Human Resources who has been trying to help Smith.

Moyo added that some of those women with problems finding housing are "good managers" and could pay their bills if they are given the chance. "But they're not even given an opportunity," Moyo said. "They have no real estate or credit references."

Nancy Skuba, chief of the social services branch of DHR that deals with Wards 5, 6, and part of Ward 8, said her staff deals with about 2,300 people a year who "are in one phase or another of a housing problem" - and Skuba deals with only about one-third of the city's caseload, she said. She added that the figure still doesn't include all those who need housing help. "Others don't even contact us at all because they have no hope and feel there's no use," Skuba said.

"I'm capable of doing many things," Smith said. "I don't want to stay on public assistance all my life. If I can get a house, I can get myself together, I can't even say where I'll be living next month. I'm always in a position to get people in trouble because they're overcrowded.