Among Rudd's many stage credits were King Lear, The Glass Menagerie, Romeo & Juliet, and Streamers.

He also starred in the television series Beacon Hill and played John Fitzgerald Kennedy in the telefilm Johnny, We Hardly Knew Ye. In addition, Rudd was a noted acting teacher.

He is survived by his wife, Martha Bannerman, their children, Graeme, Kathryn and Eliza, and his mother Kathryn Rudd.