James F. Burke, 58, the vice president of Control Data Corp. for operations in the eastern United States and the president of CDC WORLDTECH Inc., a Control Data subsidiary, died of cancer Saturday at his home in Falls Church.

Mr. Burke was born in Jersey City, N.J., graduated from Providence College in Rhode Island and served in the Pacific as a Navy officer in World War II. In 1946, he moved to New York City and went to work as an accountant for Price, Waterhouse, an accounting firm.

In 1949, he joined the Univac Division of the Sperry Rand Corp. In 1955, he was transferred to its Washington offices as assistant manager for government marketing.

Mr. Burke joined Control Data in 1965 and was named a vice president in 1974. A year later, he was named president of CDC WORLDTECH Inc., a job he held in addition to the position he held with the parent corporation.

Mr. Burke was a member of the Armed Forces Communications and Electronics Association, the Army & Navy Club in Washington, the International Club and the Military Order of the Carabao, a group of veterans of the Philippines.

Survivors include his wife, Mildred E. of Falls Church; two daughters, Maureen B. Wiesemann of Springfield, and Suzanne Burke-Ticknor of Burke, Va.; three sons, James F. Jr. of Middletown, Va., Mark X. of Winchester, Va., and Dennis of Acworth, Ga.; two sisters, Mary B. Hawley of Middletown, N.J., and Elizabeth V. Murphy of Bayonne, N.J,; three brothers, Thomas R. of Rumson, N.J., Edward M. of Glenview, Ill., and John J. of Long Beach, Calif., and two grandchildren.

The family suggests that expressions of sympathy be in the form of contributions to the Hospice of Northern Virginia Inc., Arlington, Va.