John David Burke, 27, a senior law student at Potomac School of Law and a computer specialist at the U.S. Senate Computer Center, died of cancer Friday at his home in Chevy Chase.

Mr. Burke has worked at the computer center for about two years.

Born and reared in Washington, he graduated in 1970 from Georgetown Preparatory School in Rockville, where he received letters in five sports. The College of the Holy Cross and Colgate University approached him with football scholarships but he chose instead to enter Georgetown University without a scholarship because, he said, "I don't want to get caught up in football and neglect my studies."

Mr. Burke concentrated on his studies his freshman year but found that he missed football and came out of his self-imposed retirement his sophomore year. Despite a collapsed lung in his s junior season, which nearly cut short his football days, he returned to playing with the Hoyas.

In 1975, the year he graduated from Georgetown, Mr. Burke was named an honorable mention all-American football halfback. Earlier this year, he was inducted into the Georgetown University Hall of Fame.

Mr. Burke, who lived in Chevy Chase, also wrote poetry, which appeared in high school and college publications.

Suvivors include his wife, Marilyn Marchese Burke, his parents, Drs. Frederic and Ruth Burke, all of Chevy Chase; seven brothers and sisters, Buzzy, of Cabin John, Mary Ryscavage of York, Pa., Patrick, of Denver, Francesca Burke-Johnson of Seattle, Barbara O'Brien of Chicago, and Frank and Thaddeus, both of Chevy Chase.

The family suggests that expressions of sympathy be in the form of contributions to the Vincent Lombardi Cancer Research Center at Georgetown University Hospital.