Nathaniel Graham Alcock was born in Platteville, Wisconsin, on January 18, 1881. He received his B.S. degree in 1907, his M.S. degree in 1908, and his M. D. in 1912, all at Northwestern University. He married Marjory Bates in 1912 and the couple had two daughters and one son.
Dr. Alcock joined the faculty of the State University of Iowa College of Medicine in January 1915 as the second instructor in Genito-Urinary Surgery, following the one-year appointment of instructor Lewis W. Bremerman, from 1914 to 1915. As was common practice, Alcock's appointment was part time, which allowed him to operate a part time private practice, with his office located on the second floor at 8 South Clinton Street in Iowa City, Iowa.
In 1923 Alcock established the College of Medicine Department of Urology and developed it into one of the most highly regarded teaching programs in the nation. He was known for his pioneering work in transurethral surgery during the 1930s, which was performed to relieve prostatic enlargement. He was a member of the American Urological Association and other professional societies. In 1950 he was awarded the annual medal from the Mississippi Valley Medical Society for distinguished service in his position as president from November 1949 to December 1950. Alcock, who was known by his colleagues as "the Chief" served under four University presidents during his 35 years in the College of Medicine: Thomas H. Macbride, 1915 to 1916; Walter Jessup, 1916 to 1934; Eugene Gilmore, 1934 to 1940; and Virgil M. Hancher, 1940 to 1949.
President Hancher demoted Dr. Alcock from head to acting head of the Department of Urology on July 1, 1947, due to Dr. Alcock's rejection of the Private Practice Plan, a University initiative intended to limit the amount of income that members of the College of Medicine faculty were allowed to earn through their private practices. Dr. Alcock was a member of the Medical Problem Committee during 1946 to address the Private Practice Plan, which he viewed as socialized medicine. Dr. Alcock died December 10, 1953.