The estate of architect Edward Durell Stone has in effect admitted design flaws in the construction of the Kennedy Center, including responsibility for its leaky roof, and agreed to paying the government nearly a quarter of a million dollars in damages.

The damage costs will virtually eliminate the architect's fee for design of the center. The government has refused to pay the design fee until the damage claims were settled.

Details of the agreement between the Stone estate and the government have emerged from a "stipulation of agreement" which is expected to be announced today by Chief Judge Daniel M. Friedman of the U.S. Claims Court.

The dispute dates back to 1974 when Stone's attorney's filed a claim for $295,798 in fees from the government for planning and design services it agreed to for the construction of the performing arts center.

Government attorney's, however, filed a counter claim asking for $2 million for "major errors and deficiencies" including improper beam cuts and installation of fixtures which caused leaks in the roof.

The claim further cited cracks in concrete on the adjacent plaza drive and inadequate drains and slopes for roof drainage.

In a stipulation signed by attorneys from both sides, the architect agreed to pay $248,451.94 and the government approved $223,451.94 in fees for the architect's services. The agreement would eliminate the fee and still leave the estate owing the government $25,000.

Meanwhile, the project settled with some of the contractors for the project who were also cited for damages caused by inadequate workmanship.

Stone, noted for designing such buildings as the United States pavilion at the 1958 Brussels World's Fair and the American Embassy in New Delhi, was named in 1959 to direct planning and specifications for the then-called National Cultural Center.

The $70 million project was approved in 1965 and opened six years later as the John F. Kennedy Center for the Performing Arts but has been plagued by financial troubles ever since.