The Academy of the Washington Ballet, a full-time academic and dance program for teenagers, will close its doors this June, its founder, Mary Day, announced yesterday.

The associated Washington School of the Ballet, which offers ballet classes to about 200 children and adults, will continue functioning under Day's direction.

The Academy, founded 15 years ago, has graduated such accomplished dancers as ballerina Marianna Tcherkassky of American Ballet Theater, Kevin McKenzie of the Jeffrey Ballet, Muriel Aasen of the New York City Ballet, and other principals of major companies here and abroad. Though similar schools are common in Europe, the Academy is one of very few institutions of its type in the United States.

Six of the Academy's present total of 60 students will graduate in June. The next class in line, consisting of 16 students, also has been assured of graduation, possibly this summer. Efforts are being made to assist the remaining Academy students with relocation in other area schools. Day's hops is that the majority will continue their ballet training at her School of Ballet.

About 15 teachers of the Academy's academic faculty, accounting for roughly $100,000 annually in salaries, will be let go as a result of the move. The six full-time and three part-time members of the dance faculty will remain with the ballet school.

The Academy is being closed "after painful and lengthy consideration," Day said, because of a shortage of adequate funding and a work load that has become too great for her to manage. Other reasons include the increased considering for serious arts students by public and private schools through "release time" programs, and the loss of scholarship revenue from the Washington Ballet's curtailed Christmas season "Nutcracker" performances.

Day also said she now wanted to concentrate her energies on professional training and the activities of the Washington Ballet, the pre-professional performance group under the same auspices as the Academy and the School of Ballet.

Day said that many of the Academy students and their parents were "quite sad and upset" over the closing. "They weren't entirely surprised by the news, though," she said, "since they had seen for some time that my tasks were becoming too much for one person to handle."

Annual tuition at the Academy this year was $2,850. In recent years, over $30,000 has been awarded in scholarships annually, largely from receipts from the Washington Ballet's "Nutcracker."

Mary Day and her former teacher, Lisa Gardiner, both native Washingtonians, founded the Washington School of Ballet in 1944. Performing activities date from 1949, when Washington Ballet dancers first appeared with the National Symphony. The Academy was founded in 1962, after Day's trip to the Soviet Union to study teaching methods there under State Department auspices. The newly reconstituted Washington Ballet is scheduled to perform a series of programs at Lisner Auditorium this year on Feb. 20, March 13 and May 1.