Two hypotheses compete to explain the remarkable topography and geoid of the Tharsis province on Mars: One attributes Tharsis to volcanically constructed surface loads, whereas the second views it as dynamic effects of single-plume mantle convection. Both are likely to contribute, so we would like to constrain both. We introduce a method to invert load structure from geoid and topography of a viscoelastic planetary body. Estimates of the internal load contribution to Tharsis depend on assumed parameters. Buoyancy of the internal load estimate increases with increasing lithospheric thickness, crustal density, and crustal thickness, and load size increases with depth of loading. Despite parameter uncertainties, we can rule out a predominantly internal load. We cannot reject the possibility that Tharsis results from surface loading alone. Internal loads contribute at most 35% of the lithospheric force balance, 50% of the topography, and 25% of the geoid at Tharsis, for load depths ≤420 km and lithospheric thickness Te ≤ 200 km. A corollary is that any Te and reference density structure can exactly reproduce the geoid and topography if internal loading can vary as a function of harmonic degree and order. Hence Te and density estimates depend on assumptions about internal loading. If surface and internal loads are approximately uncorrelated, Te is ~110 km with crustal density ~2600 kg m-3. Adopting these parameters, internal buoyancy contributes 2.1% of lithospheric loading, 4.2% of topography, and 0.7% of the geoid at Tharsis for a 200 km deep load, or 4.3% of lithospheric loading, 8.5% of topography, and 2.2% of the geoid for a load at 400 km depth.