Stuart has appeared in many productions both in the US and in the United Kingdom. From playing Cord Elam at the National Theatre in Oklahoma with Hugh Jackman to appearing as Tommy Boatright in The Normal Heart with Martin Sheen.

Trevor Nunn directed Stuart at the Southwark Playhouse in Desert and Diamond at the Edinburgh Festival directed by Jane Moriarty. Along with Mark Strong and Elizabeth Debbicki, Stuart appeared in The Red Barn at the National Theatre.

Among his other theatre work is Bishop Paul Marcinkus in The Last Confession with David Suchet, Gyp DeCarlo in Jersey Boys at the Prince Edward Theatre in the West End, Joe Keller in All My Sons at the Royal Lyceum Theatre in Edinburgh, Mr. Robinson in The Graduate with Amanda Donahoe, Walter in The Price in Manchester, and Bishop Paul Marcinkus in The Last Confession with David Suchet which was at the Royal Haymarket Theatre in the West End.