Benton, whose recent stage credits include Hairspray and Filter's A Midsummer Night's Dream, will play Mr Stuart, while Evans, who has previously starred in Blood Brothers in the West End, will play Ms Mason.
Also joining the principal cast are Stewart Clarke as Jonny, Luke Fetherston as Goose, Joshua Dowen as Louis, Harry Francis as Davey, Hannah Levane as Paulette, Bronte Barbe as Sharon and Lucinda Lawrence as Rhonda.
The ensemble also includes James Darch, Fela Lufadeju, Katy Hards, Lisa Ritchie, Jak Allen Anderson, Joseph O'Reilly, Danielle Mullan, Simone Murphy and Parisa Shahmir.
Gray and Sidwell also starred in the one-off gala concert of Cool Rider at the Lyric Theatre in January.
The story of Cool Rider takes place two years after the original film at Rydell High School, and features a new cast of characters.
Songs include "Who's That Guy?", "Score Tonight", "Cool Rider", "Girl for all Seasons" and "Rock-a-Hula Luau (Summer Is Coming)".
Cool Rider runs at the Duchess Theatre from 15 to 19 April 2014.