William B. Franke, 85, who was secretary of the Navy from 1959 to 1961 and advocate of a modern naval defense system, died Saturday at a Rutland, Vt. Hospital of complications following gall bladder surgery.

Mr. Franke succeeded Thomas S. Gates Jr. as secretary of the Navy in 1959. He received his first presidential appointment in 1954, when he became assistant secretary of the Navy for financial management.He then served two years as undersecretary of the Navy, from 1957 to 1959.

One of Mr. Frank's main objectives as secretary of the Navy was the implementation of a nuclear-powered, missile-launching fleet, and elimination of older craft. As undersecretary of the Navy, he headed a six-month study to create a new bureau of naval weapons as part of a reorganization to prepare for the nuclear-missile age.

Mr. Franke was a member of the "Doolittle Group," headed by Lt. Gen. James Doolittle, to examine the operations of the Central Intelligence Agency.

From 1948 to 1951, he was auditing chair of the Army comptrollers Civilian Panel, which helped the Army reorganize its system of spending controls.

Mr. Franke was born in Troy, N.Y., and graduated from Pace College in New York City. He became a certified public accountant in 1924 and founded his own accounting firm, Franke, Hannon & Withney, of Troy and New York City, in 1929.

In 1948, he received a doctor of science degree from the University of Louisville and a doctor of civil law degree from Pace College in 1955.

Mr. Franke's other awards included the Patriotic Civilian Service commendation from the Army, the Distinguished Service Award from the Department of Defense and the Medal of Freedom.

He lived in Rutland, Vt., and was director emertus and investment consultant, as well as a member of the advisory board, of the Howard Bank in Rutland.

His wife of 51 years, the former Bertha Irene Reedy, died in 1970.

Survivors include three daughters, Phyllis Fowler, of Fort Mill, S.C., Anne Ulinski, of McLean, and Patricia Kouns, of Knoxville, and nine grandchildren. CAPTION: Picture, WILLIAM B. FRANKE, 1959 Photo