Observations of the distribution of tectonic features and their relationship to local surface topography indicate that the floor of the oldest and largest crater of the summit caldera of Mars' Olympus Mons volcano may have undergone subsidence in response to depressurization of a subsurface magma chamber. In this study, we construct an axisymmetric finite element model to calculate elastic stresses in a volcanic edifice to investigate the relationship between surface tectonism, caldera subsidence, and the physical characteristics of Olympus Mons' magmatic reservoir. Constraints on the model are provided by the stress field within the crater indicated by the distribution of radial ridges and circumferential graben that we hypothesize formed due to a postcollapse and postresurfacing phase of subsidence of the caldera floor. Model results show that the surface stress state is not strongly sensitive to the aspect ratio or pressure distribution of the magma chamber, or to the contrast in stiffness between the magma chamber and surroundings, but is strongly dependent on the width and depth of the chamber. For a range of plausible model parameters, we find the maximum depth to the top of the magma chamber to have been ≤16 km, which indicates that the chamber, at the time of crater floor subsidence, was positioned within the Olympus Mons edifice, at a level much shallower than the estimated source depth of Martian magmas (∼140–200 km). The allowable range of solutions indicates that the vertical position of the magma chamber may have been controlled by the neutral buoyancy level of ascending magma. Our results suggest a gross similarity between the configurations of the magmatic plumbing systems of Olympus Mons and several well-studied terrestrial volcanoes such as the Hawaiian shields.