The geodynamical response of the lithosphere under stresses imposed by the geologically young north polar cap is one of the few clues we have to constrain both its composition and the present-day thermal state of Mars. Here we combine data from orbital radar sounders with a lithospheric loading model to self-consistently estimate the density (ρ) and real dielectric constant (ε) of the polar cap, and the elastic thickness of the lithosphere underneath (Te). We show that ρ can range from 920 to 1520 kg m, ε is constrained to be 2.75 (+0.40,-0.35), and Te is found to range from 330 to 450 km. We determine an updated polar cap volume that is up to 30% larger than current estimates that all neglect lithospheric flexure. Inferred compositions suggest that a minimum of 10% CO is buried in the deposits, which may have important implications for the climate evolution of Mars.