The flexure of the lithosphere under stresses imposed by the geologically young south polar cap is one of the few clues we have regarding the south polar cap composition and the present-day thermal state of Mars. Here, we combine radar, gravity, and topography data with a flexural loading model to estimate the bulk density (ρ) and average real dielectric constant (ε') of the south polar cap, and the elastic thickness of the lithosphere (Te). Given the uncertainties of the data, our results constrain ρ to be 1,100-1,300 kg m−3 (best fit of 1,220 kg m−3), ε' to be 2.5-3.4 (best fit of 3.3), and Te to be greater than 150 km (best fit of 360 km). Based on these results, the maximum lithospheric flexure is 770 m, and the polar cap volume could be up to 26% larger than previous estimates that did not account for lithospheric flexure. Our inferred compositions imply that the dust concentration would be at least 9 vol% if the CO2 ice content were negligible, and that the CO2 ice concentration would be more than the known 1 vol% CO2 if the dust concentration were less than 9 vol%. The 1-σ lower limit on Te implies a surface heat flow that is less than 23.5 mW m−2. This lower limit is significantly less than the range of acceptable values at the north pole (330-450 km, heat flow of 11-16 mW m−2), and helps satisfy global thermal evolution simulations that predict hemispheric differences in surface heat flow.