The main theater at Petra is cut a slope above the riverbed of Wadi Mousa,  600 m. from the center of the city. Earlier tombs on that cliff were destroyed in order to accommodate the theater at that site. It is dated to the time of the Nabataean ruler Aretas IV (r. 9 BCE-40 CE), and was excavated in 1961-1962. The cavea (auditorium) and orchestra area were cut out of the rock, while the scaena (stage building) was constructed of ashlar and faced with white-mottled breccia. The theater faces east and follows the plan typical of the Greco-Roman world, and the cavea seated approximately 4,000 people. The theater was remodeled during the 1st and 2nd centuries CE, one of the few major architectural changes at Petra made during the Roman occupation.

Sources:

Hammond, Philip C. "Petra." Grove Art Online. Oxford Art Online. Oxford University Press, accessed January 12, 2015, http://www.oxfordartonline.com/subscriber/article/grove/art/T066760.

Segal, Arthur. Theatres in Roman Palestine and Provincia Arabia, 91-92. Leiden: E.J. Brill, 1994.