The Reagan Administration has tangled the nation's food stamp program in so much red tape that it cannot fully help those it was designed to serve, according to a Harvard School of Public Health study released yesterday.

The paperwork required for food stamp recipients and administrators has increased so dramatically during the last five years that the program's effectiveness has been impaired, concluded the Physician Task Force on Hunger in America. The group drew national attention through an earlier study released in January when it identified 150 American "hunger counties" in which only one-third of eligible citizens receive food stamps.

The group concluded that Congress should step in to reduce the regulations governing the program. The group includes two School of Public Health officials, J. Larry Brown, an administrator, and Professor of Health Policy Julian B. Richmond.

"We found that there are a series of administrative barriers which prevent state and local administrators from helping people," said Brown, who heads the group.

Assistant Secretary of Agriculture John W. Bode last month sharply attacked the January report, on which the new report was based, calling it "Grossly innaccurate."

The food stamp program does not now serve a smaller proportion of eligible people than it did five years ago, said Bode, who last month wrote a letter to President Derek C. Bok criticizing the task force's earlier "hunger county" report.

Bode cited Department of Agriculture statistics indicating that the fraction of eligible people receiving food stamps has risen from 45 percent to 62 percent since 1979.

The food stamp program, created by Congress in 1964, currently helps nearly 20 million Americans buy food, but another 10 to 15 million eligible people do not receive benefits, according to federal estimates. Brown said recently enacted federal regulations have causes the fraction of eligible people who receive benefits to decline.

In 1981, the federal Department of Agriculture, which runs the food stamp program, instituted a number of changes in the program to cut back program waste.

The report, which was funded in part by grants from USA for Africa and the Pillsbury Company, particularly criticized the food stamp application forms for being as long and as complex as the income tax long-form, and for making more than 100 rule changes within the last three years.

The 21-member hunger task force also found that 40 to 45 percent of the eligible people don't apply to receive food stamps because they don't know they can participate in the program.

According to the report of the Harvard-linked group, during the past five years the number of Americans receiving food stamps has tumbled at a time when the number of Americans living below the poverty line has increased.