The show's producers announced the casting Wednesday for the Signature Theatre production, which is being directed by Daniel Aukin.
The staging is to run Aug. 7 through Sept. 16 in The Irene Diamond Stage at The Pershing Square Signature Center off-Broadway.
"Sally lives with her mysterious family in a cavernous home overlooking Los Angeles. When a visitor arrives, Sally's dark secrets -- and the secrets of those around her -- threaten to come into the light," a synopsis said.
Shepard's plays include "La Turista," "Paris, Texas," "Buried Child" and "True West."