On stage Burke appeared in several productions by the Royal Shakespeare Company, including Richard II, Romeo and Juliet, Roberto Zucco, The Tempest, Peer Gynt, Measure for Measure, Troilus and Cressida, Two Shakespearean Actors, All's Well That Ends Well and Antony and Cleopatra. In 2008 he appeared at the National Theatre as the Shepherd in a new version of Sophocles' Oedipus by Frank McGuinness.