Shepard wrote more than 40 plays and won the Pulitzer Prize for drama for Buried Child in 1979.
He went on to be nominated for the best supporting actor Oscar for 1983's The Right Stuff and starred in films like Black Hawk Down as well as co-writing 1984's Paris, Texas.
He died at home in Kentucky on Thursday, his family have confirmed.
Shepard's death came after he experienced complications from motor neurone disease, also known as ALS.