Isostatically compensated crustal thickness variations and associated topographic contrasts at the surface of a planet result in lateral pressure gradients, which may cause the lower crust to flow and reduce the relief. Areas of thicker crust are generally associated with more rapid relaxation of topography. On Mars, topographic features such as impact basins and the hemispheric dichotomy have survived for 4 Gyr. We use a finite difference representation of depth-dependent, non-Newtonian lower crustal flow to investigate how topography decays with time. For a dry diabase rheology, total radiogenic concentrations ≥80% of terrestrial values, and crustal radiogenic concentrations similar to terrestrial basalts, we find that an upper bound on the mean planetary crustal thickness is ~100 km. In the probably unrealistic case where all the radiogenic elements are in the crust, this maximum crustal thickness can be increased to ~115 km. The main uncertainty in these results is the total radiogenic abundances on Mars. Comparing our results with the observed shape of the crustal dichotomy provides no evidence that this slope is primarily the result of lower crustal flow. Both Hellas and the dichotomy are isostatically compensated; if the mechanism is Airy isostasy, then the lower bound on mean crustal thickness is ~30 km. Crustal thicknesses of 30--100 km on Mars can be produced by mid-ocean ridge spreading at potential temperatures of 1350¿--1600 ¿C. However, for such crustal thicknesses the lithosphere is likely to be positively buoyant, making subduction difficult. ¿ 2001 American Geophysical Union