On the flanks of Olympus Mons is a series of terraces, concentrically distributed around the caldera. Their morphology and location suggest that they could be thrust faults caused by compressional failure of the cone. In an attempt to understand the mechanism of faulting and the possible influences of the interior structure of Olympus Mons, we have constructed a numerical model for elastic stresses within a Martian volcano. In the absence of internal pressurization, the middle slopes of the cone are subjected to compressional stress, appropriate to the formation of thrust faults. These stresses for Olympus Mons are ∼250 MPa. If a vacant magma chamber is contained within the cone, the region of maximum compressional stress is extended toward the base of the cone. If the magma chamber is pressurized, extensional stresses occur at the summit and on the upper slopes of the cone. For a filled but unpressurized magma chamber, the observed positions of the faults agree well with the calculated region of high compressional stress. Three other volcanoes on Mars, Ascraeus Mons, Arsia Mons, and Pavonis Mons, possess similar terraces. Extending our analysis to other Martian volcanoes, we find that only these three and Olympus Mons have flank stresses that exceed the compressional failure strength of basalt, lending support to the view that the terraces on all four are thrust faults.