Keith Gilbert Burke, 19, a shoe store official who was injured April 15 when his struck a tree and a light post in Fairfax Country, died Tuesday at Mount Vernon Hosptial.

Fairfax Country police said the accident happened at Collingwood Road and Linfield Drive not far from the hospital where Mr. Burke was a patient in the intensive care unit until his death. He had suffered multiple fractures and internal injuries.

He was a lifelong resident of Alexandria and attended Bishop Ireton High School and Fort Hunt High School, where he graduated in 1978. Mr Burke became an employe of the Columbia Shoe Store at the Belle View Shopping Center in Alexandria a year ago and was assistant manager at the time of the accident. He was a member of St. Mary's Catholic Church, Alexandria.

He is survived by his parents, Mr. and Mrs. Francis J. Burke, and two sisters, Jan Marie and Gina Marie, all of the home in Alexandria; two brothers, Francis J, III, of Philadelphia, and Richard M., of Pensacola, Fla., and his grandmothers, Pauline A Burke and Ann DiNicola, both of Alexandria.

The family suggests that expressions of sympathy be in the form of contributions to the intensive care unit of Mount Vernon Hospital. CAPTION: Picture, KEITH GILBERT BURKE