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Turner will play Jean Grey, Shipp will portray Storm, and Sheridan will play Cyclops in the film, reports variety.com.
Director Bryan Singer posted the news on Twitter Thursday.
“Meet our new and brilliant young mutants: @Alexshipppp as #Storm @SophieT as #JeanGrey and @TyeSheridan as #Cyclops. #XmenApocalypse,” he wrote.
Oscar Issac was previously cast as the titular villain in the comicbook movie.
“X-Men” veterans Jennifer Lawrence, James McAvoy and Michael Fassebender will return for the next installment.
The film is expected to release May 27, 2016.