Shakespeare’s battle-of-the-sexes comedy The Taming Of The Shrew has been a reliable crowd-pleaser over the decades of free Shakespeare in Central Park (among the most memorable were Meryl Streep and the late Raul Julia in 1978, and Tracy Ullman and Morgan Freeman in 1990). The production that will launch the coming summer season of the Public Theater’s annual stand at the Delacorte Theater should be no exception. Expect a few unexpected twists, however: When Petruchio, who has “come to wive it wealthily in Padua” instructs his recalcitrant intended to “kiss me, Kate,” the clinch will feature Cush Jumbo and Janet McTeer in Phylidda Lloyd’s all-female staging of the play.

The three Brits are quite familiar to New York audiences: Jumbo made her Broadway debut opposite Hugh Jackman in The River and then performed her tour-de-force show Josephine And I at the Public before becoming a series regular this past season as Juliana Margulies’ new law partner on The Good Wife. McTeer, a Tony, Golden Globe and Olivier Award winner and two-time Oscar nominee, has been seen on Broadway in God Of Carnage and A Doll’s House. And Lloyd has made a specialty of reversing Elizabethan tradition by casting Shakespeare’s plays with women in all roles. Those productions, seen at Brooklyn’s St. Ann’s Warehouse, have included Henry IV and Julius Caesar. She also staged Josephine And I, and her films include Mamma Mia! and The Iron Lady.

The production is slated to run May 24 through June 26, in a season commemorating the 400th anniversary of Shakespeare’s death. The second show will be Daniel Sullivan’s updated staging of the less-well-known drama Troilus And Cressida, a war-torn romance set in ancient Greece. Sullivan is a Tony-winning Shakespeare specialist and Public Theater regular whose work has included the Al Pacino The Merchant Of Venice, among many others. Troilus will run July 19 through August 14. Casting will be announced later.

The Public also announced two more key parts of its summer program: In September, the Delacorte will be home to a brief run of a new adaptation of Twelfth Night conceived by Kwame Kwei-Armah and Shaina Taub, with music and lyrics by Taub and staging by Kwei-Armah. At the Public’s Astor Place home base, the Mobile Unit will present Romeo & Juliet, staged by Lear deBessonet, from April 11 through May 1, following a free tour of the five boroughs.

“Four hundred years after Shakespeare’s death, he continues to be central to our understanding of ourselves,” Eustis said in the summer-season announcement. “Phyllida Lloyd’s all-female version of The Taming Of The Shrew and Dan Sullivan’s modern take on Shakespeare’s tale of perpetual war, Troilus and Cressida, are this summer’s blazing contributions to our ongoing dialogue with the greatest writer in the English language.”