From all sections of Washington, about 2,000 poor people -- some shoving, some fighting mad and nearly all frantic with worry -- overflowed two District housing offices yesterday to apply for rent subsidies being offered for only 126 apartments.

"All I could think of was Cincinnati," said deputy city housing director James Clay of the crush at one office. "It kept going through my head," he said, alluding to the deaths in that city of 11 people recently amid pushing and shoving to get into a rock concert.

Yesterday's turnout at the two housing offices vividly illustrated the city's housing crisis as many of the hundreds of people who were turned away spoke angrily of their overcrowded housing and rents that are more than they can afford.

"I need a large place bad," said Louise Easterling, who lives with her three children and four grandchilren in one room she rents from a friend in a house on New Jersey Avenue NW.

Easterling arrived at the city housing office at 2901 14st St NW, blanket in hand, at 2 a.m. yesterday. She was first in line.

Long before 8:30 a.m., when the city was going to begin accepting the applications for the few subsidies available, the crowd jammed the small lobby of the gingerbread Victorian building and spilled out onto 14th and Harvard streets.

Patricia Whitfield, 23, left the three-bedroom public apartment projects in Far Northeast that she shares with nine other people at about 7 a.m. yesterday. She dropped off two of her children at nursery school and boarded the bus on Nannie Helen Burroughs Avenue NE with her 8-month-old son. When she arrived at the second of the two offices, at 2051 Martin Luther King Ave. SE. to apply for a subsidy she was the 733rd person in line.

The crowd at both offices was mostly black and mostly female. There were singles and families, young and old. They carried babies and totted blankets and some slept part of the night on matresses and coffee tables outside the government doors.

City officials had announced last week that, for the first time in a year, residents could apply for the federal rent subsidy program. The program, financed by the Department of Housing and Urban Development, enables tenants to select their own housing and pay no more than one-fourth of their income in rent. HUD pays the balance to the owner.

The program has strict income guidelines that permit, for example, a family of four to earn no more than $19,350 a year to qualify.

The city announced in letters to about 1,000 people who had expressed an interest in the subsidies and through the news media that there would be a one-day registration from 8:30 a.m. to 6 p.m. Only 250 applications would be accepted at each site on a first-come, first-serve basis.

This year, HUD allocated to the city subsidies for 161 families. Thirty-five were for three-bedroom apartments or houses that already had a waiting list of 170 families. The tenants yesterday were to be permitted to apply for the remaining subsidies.

Under the program, HUD has offered to pay subsidies for 52 efficiency apartments, 10 one-bedrooms, 44 two-bedrooms, 10 four-bedrooms and 10 five-bedrooms.

District officials said 570 families in the city currently receive such subsidies to rent apartments in private housing. Registration was closed a year ago because there were waiting lists of eligible families, officials said.

Because of the crowds, city officials at the 14th Street office decided yesterday to send everybody home shortly after 9 a.m. rather than try to accept applications. Those persons who succeeded in signing their names and addresses on legal-pad lists that were circulated were told they would be called individually within the next seven days.

Jim Woolfork, acting administrator of the city's housing division, which operates the rent subsidy program, called the change in plans a "battlefield decision."

At 2051 Martin Luther King Jr. Ave. SE, the mid-morning scene was much more orderly. Frustration was evident, but those waiting in a line that snaked through a large parking lot said the process was much more calm there than at 14th Street.

The 900-odd people who showed up in Southeast were given numbers. Applications were accepted from all, a process that lasted hours. Housing officials said priority would go to the first 250 persons signed up at each site as promised, but that the others would be placed on waiting lists for other housing or subsidy money as it becomes available -- which could mean a wait of years for most.

Many persons interviewed, particularly at the 14th Street office, criticized the way the city handled the application process and left them with little hope that they would get help. Some said they had taken leave from their jobs to stand in line.

Eleanor Thomas, a mother of six, said she had been on the public housing waiting list in the city since 1967. She and her children, one of them handicapped, live with Thomas' father in a one-bedroom apartment on H Street NE. Twice recently they have been forced to move because of overcrowding.

"It's always been the case," said Thomas, a supply technician for the Defense Department who receives no public assistance money. "I haven't been able to find anything."

Judy McDaniels said the bathroom ceiling in her apartment has caved in and she is seeking a better place for her and her family. She arrived yesterday at the 14th Street office at 6:45 a.m., and left near tears at 8 a.m., when she was told no applications would be accepted.

"It's just not fair," she said. "I keep trying to get a place, but it's hard. I just want somewhere that's comfortable to live, anywhere."