The combined effects of compressive stress, applied pressure, and edge folding of a freestanding thin film have been theoretically investigated on the buckle morphologies of the structure. In the framework of the Föppl-von Kármán theory of thin plates, the different buckle profiles have been analytically determined, and two buckling regimes have been identified for the film: one regime where the transition from upward to downward buckling is continuous, and one that is discontinuous (snap-through). The critical pressures characterizing the different regimes have then been determined, and an hysteresis cycle has been identified through the study of buckling versus pressure. The case in which the thin film is deposited on a substrate has also been discussed.