Robert Phelps worked with the California Shakespeare Festival from 1966 to 1970 as an Equity Apprentice for two seasons, as an Equity Journeyman for two seasons, and as a member of the Master Company in his fifth year with the Company. Later that year, he began study at Carnegie Mellon University, graduating in 1972 with a BFA degree in Acting. In 1972, he joined the New Phoenix Repertory Company, appearing in the Broadway productions of "The Great God Brown" by Eugene O'Neill directed by Hal Prince, and "Don Juan" by Moliere directed by Stephen Porter. In addition to his work in film and television, he was in the original cast of the long-running Off-Broadway production of "Moonchildren," and appeared in regional theatre productions around the country.