Play titles are considered longer works of literature and should be underlined. The general rule of thumb is that if the work can stand on its own and is not a part of another work, it should be underlined or italicized.
Italics can be used instead of underlining, but a title should not be both italicized and underlined. Also, the titles of books and magazines, long musical pieces, movies and television shows, artwork, long poems, pamphlets and famous speeches should be underlined. Shorter works, such as short stories or television episodes, should be surrounded by quotation marks rather than italicized or underlined.