Geophysical models of flexural stresses in an elastic lithosphere due to an axisymmetric surface load typically predict a transition with increased distance from the center of the load of radial thrust faults to strike-slip faults to concentric normal faults. These model predictions are in conflict with the absence of annular zones of strike-slip faults around prominent loads such as lunar maria, Martian volcanoes, and the Martian Tharsis rise. We suggest that this paradox arises from difficulties in relating failure criteria for brittle rocks to the stress models. Indications that model stresses are inappropriate for use in fault-type prediction include (1) tensile principal stresses larger than realistic values of rock tensile strength, and/or (2) stress differences significantly larger than those allowed by rock-strength criteria. Predictions of surface faulting that are consistent with observations can be obtained instead by using tensile and shear failure criteria, along with calculated stress differences and trajectories, with model stress states not greatly in excess of the maximum allowed by rock fracture criteria. ¿ American Geophysical Union 1994