Dr. Joseph A. Kiesel, 55, board chairman of the Northern Virginia Doctors Hospital in Arlington who had practiced internal medicine in Northern Virginia and taught clinical medicine at Georgetown University's medical school since 1953, died Friday at Northern Virginia Doctors Hospital. He had cancer.

He was a founder of the Northern Virginia Doctors Hospital and had served on the hospital's board since 1956. He was a past-treasurer of the Northern Virginia Doctors Hospital Corporation and was chairman of the corporation's board of directors at the time of his death.

Dr. Kiesel was a 1949 graduate of Georgetown University's Medical School, and had taught at the school since 1953. He was an assistant professor of clinical medicine at the time of his death.

He was a native of New York City where he attended Fordham University. He had served in the Air Force for two years before beginning his practice in internal medicine in 1953. His offers were in Arlington. Dr. Kiesel lived in McLean.

Dr. Kiesel was a member of the Knights of Columbus. His professional memberships included the Georgetown Clinical Society, the Internal Medicine Society, and the Fairfax and Arlington medical societies.

Survivors include his wife, Elizabeth F., of McLean; two sons, Joseph N. II, of Dale City, and John J., of McLean; seven daughters, Ann M. Garbak of Arlington, Mary E. K. Miller and Kathleen Pieslor, both of Annandale, and Elizabeth A., Margaret L., Virginia E., and Teresa A. Kiesel, all of McLean; a sister, Elleen F. Giaimo of the Azores, Portugal; a brother, Dr. Robert D., of Falls Church, and one grandchild.