A lawsuit filed yesterday on behalf of a group of low-income people alleges that the District government has violated the federal food stamp law and has kept them and thousands of other poor people from obtaining food stamps as quickly as the law requires.

The lawsuit, pending before U.S. District Judge Stanley Sporkin, seeks a preliminary injunction ordering the D.C. Department of Human Services, which administers the federal food stamp program, to immediately begin providing food stamps to eligible applicants within the periods set by law.

The lawsuit is intended to "stop food stamp runaround," said Susanne Sinclair-Smith, director of the Washington Legal Clinic for the Homeless, one of the nonprofit groups that has been compiling information for the case.

Federal law stipulates that food stamps be available to the typical applicant within 30 days after the person applies and within five days in hardship cases. Among those who typically qualify for expedited food stamp benefits are homeless people and those receiving aid for families with dependent children.

But the five plaintiffs in the lawsuit said they had to wait up to 60 days to get food stamps that they should have received in five days.

The plaintiffs are Marcia Slayton, an unemployed mother of three who lives with her disabled aunt; Gregory L. Mitchell, 26, who is homeless and the father of a 10-year-old son; Veronica Franklin, 28, a mother of two who also is homeless; Mary H. Clark, an unemployed, disabled woman who lives in a Northwest boardinghouse; and Nubassa Kenyatta, another homeless man.

The action was filed by a team of lawyers from the Washington Legal Clinic, Neighborhood Legal Services and the law firm of Kirkpatrick & Lockhart.

"What we are finding is that food stamp offices are so understaffed and so poorly managed that their practices in handling applications for food stamps are arbitrary," Sinclair-Smith said. "As a result, there are quota systems, odd hours . . . arbitrary, unwritten rules and practices."

In the petition, the plaintiffs ask that the lawsuit be declared a class action that could benefit an estimated 30,000 homeless and other low-income people in the District.

Food stamp coupons are paid for with federal money, program administrators said. The federal government also pays 50 percent of the cost for the staff that administers the local food stamp program; the city pays the other 50 percent.

Named as defendants in the case are Mayor Marion Barry, who has responsibility for District compliance with the federal food stamp law; N. Anthony Calhoun, director of the Department of Human Services; and the U.S. Department of Agriculture, the agency responsible for ensuring that the District follows the food stamp law.

Attorney Frank Trinity said a March 1989 report prepared by Kathleen Dockett for the University of the District of Columbia found that only about 5 percent of the homeless people on Washington's streets received food stamps.

Bread for the City, a social ministry, recently was awarded $50,000 from the federal Community Food and Nutrition program to sign people up for food stamps. A program administrator said that all of the people who come to Bread for the City for food are eligible for food stamps but that only about a third use them.

James Butts, chief of the Department of Human Services income maintenance administration, said he couldn't comment on the lawsuit because he hadn't seen the court papers yet. "But it is our desire and intent to comply with the federal law and the District law as well," he said.

Butts said he was unaware of any case in which there was a delay in issuing food stamps to a qualified applicant.

However, city benefit programs have been strained in recent months by the "tremendous increase in application for benefits . . . . It has been a problem to process applications as expeditiously as we would like," Butts said. He said the increased applications reflect the area's high unemployment and the economic downturn.

"The businesses that normally would hire low-income, unskilled persons are not hiring, and those people have turned to the public welfare agencies for assistance," he said.

The city provides food stamps to about 72,000 people each month, Butts said. "But we are seeing increases in all our programs," he said, "and if the trend continues, I anticipate as much as a 10 percent increase by the end of the fiscal year."