Wilbur C. Gilliam, 58, the regional director for local claims of the Criterion Insurance Co. here, died Sunday at Suburban Hospital in Bethesda. He had cancer.

Mr. Gilliam spent more than 30 years in the insurance industry and was a specialist in claims. He joined the Glens Falls Insurance Co. in South Carolina in 1949 and worked for that company in Michigan and Kentucky before moving to the Washington area in 1957. He was district manager for Glens Falls here and handled claims involving automobiles, surety bonds and other types of insurance.

About 1970, he joined Criterion. Most of his work there involved automobile claims.

Mr. Gilliam was born in Roanoke, Va., and earned as associate of arts degree from the College of William & Mary. He served in the Pacific with the Marine Corps during World War II. He worked for Western Union in Richmond before joining the Glens Falls company in South Carolina.

Mr. Gilliam was a former member of the Lakewood Country Club and played golf there and at the Glendale Golf Club.

Survivors include his wife, Jean, of Silver Spring, where the family lived; a daughter, Nancy Anne Worthington, of San Francisco; a son, Wilbur C. III, of Lexington, Ky., and a sister, Mrs. W. E. Pearce III, of Richmond.