Shelley first broke out on the Broadway scene with roles in Neil Simon's The Odd Couple and Noël Coward's Sweet Potato and Hay Fever. In 1974 she appeared in the Broadway premiere of Alan Ayckbourn's comedy Absurd Person Singular. The all-star cast also featured Richard Kiley, Sandy Dennis, Geraldine Page, Larry Blyden and Tony Roberts.
The production opened Oct. 8, 1974, at the Music Box Theatre. The New York Times' Clive Barnes called it "the best light comedy Britain has sent us in years and years" and praised the cast's "uniformly excellent" performances.
Five years later Shelley starred in Bernard Pomerance's The Elephant Man, which transferred to Broadway after an Off-Broadway production at the York Theatre at St. Peter's. She played Mrs. Kendal opposite Philip Anglim as John Merrick and Kevin Conway as Frederick Treves.
The play made its Broadway debut April 19, 1979, at the Booth Theatre. Critic Richard Eder commended the "array of shining performances" in his review for the New York Times. "While Philip Anglim, as the deformed innocent, is as remarkable as ever," he wrote, " Carole Shelley's witty and passionate performance as the actress who reaches out to him has grown even more exuberant."
Shelley won the 1979 Tony Award for Best Actress in a Play in a tie with Constance Cummings in Wings, and the production took home the top prize of Best Play. Notable replacements during the show's 916-performance run include David Bowie and Mark Hamill.
In the 1990s Shelley began appearing in musicals, taking on roles in Show Boat and Cabaret. In 2003 she originated the role of Madame Morrible in the mega-hit musical Wicked. Her last Broadway role to date was in Billy Elliot: The Musical. She played Grandma in a cast that included Gregory Jbara, Haydn Gwynne and Santino Fontana. David Alvarez, Trent Kowalik and Kiril Kulish shared the role of Billy.
Billy Elliot opened Nov. 13, 2008, at Broadway's Imperial Theatre and was a critical and commercial success. It was nominated for 15 Tony Awards, including Best Featured Actress in a Musical for Shelley, and won ten. Billy Elliot is tied with The Producers for the musical production with the most Tony Award nominations.