Cleveland R. Chambliss, 59, an associate director for health planning with the U.S. Public Health Service, died Monday at Howard University Hospital after a heart attack.

He had held that position since 1976. He was associate director for program coordination in the bureau of health planning and resources development of the health resources administration.

Before that, Mr. Chambliss had been on assignment for two years to the National Academy of Sciences, participating in a study on health care resources in the Veterans Administration.

Beginning in 1947 as an administrative intern at the old Freedmen's Hospital, now Howard University Hospital, he went on to become hospital administrative officer at Freedmen's in 1954. He remained there until 1964.

Mr. Chambliss then joined the National Institutes of Health as an assistant chief of the plant safety branch, and held several other positions with the Department of Health, Education and Welfare.

He was born in Jackson, Miss. He graduated from West Virginia State College, received a master's degree in hosptital administration from Northwestern University and a law degree from Georgetown University. He also took graduate work at American and Harvard universities and the University of Maine.

He was a member of the D. C. and West Virginia bars and the American Bar Association. He was an Army Air Force veteran of World War II.

Mr. Chambliss belonged to the D.C. Public Health Advisory Committee, the American Association for the Advancement of Science, the American College of Hospital Administrators, the Maryland-District of Columbia-Delaware Hospital Association, and the D.C. Health and Welfare Council. He was a founding member of the Association of Assistant Administrators.

He had received a number of honors, including the Superior Performance Award of USPHS.

He is survived by his wife. Dr. Harriette Clark Chambliss, and two sons, Cleveland R. Jr. and Marque, all of the home in Washington: his mother, Celestia Chambliss, and a sister, Regina Lynch, both of Los Angeles; two other sisters, Celestia Porter, of Memphis, Tenn., and SibyI Moses, of Newark, N.J., and two brothers, Edgar, of Detroit, and Marque, of Jackson.