McCune graduated from the University of Missouri School of Law in 1929 and started a practice in Tulsa.

He served as an assistant city attorney from 1940 to 1942 when he joined the U.S. Army during World War II.

After the war he was appointed assistant United States attorney for the Northern District of Oklahoma where he served between 1945 and 1952.

Later in his tenure, he served as the chair of the judiciary committee and authored substantial reforms of Oklahoma's legal system.

[2] He lost his reelection campaign in 1972 to a primary challenge from Mandell Matheson.