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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 the polar cap composition and the present‐day thermal state of Mars. Here we combine radar data with a flexural 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). Our results show that ρ ranges from 920 to 1,520 kg m −3, ε′ is 2.75 (+0.40, −0.35), and Te is between 330 and 450 km. We determine a polar cap volume that is up to 30% larger than current estimates that all neglect lithospheric flexure. Our inferred compositions suggest that, for dust content larger than about 6 vol%, 10 vol% CO 2 ice is mixed within the polar deposits, which has important implications for the climate evolution of Mars. Plain Language Summary: The north polar cap of Mars is a tremendous reservoir of ices and dust of unknown concentration and composition. It is transparent to radar giving us a unique insight into its structure and composition. Here we use a novel technique that combines radar and elevation data along with a flexure model, to invert for the polar cap composition and the strength of the underlying lithosphere. Similar to previous studies, we find that the lithosphere below the north pole is extremely rigid and does not deform much under the load of the polar cap. This implies that the north polar region is currently colder than the rest of the planet, which has profound implications for our understanding of the structure and evolution of the Martian interior. Our inferred compositions suggest that for reasonable dust contents, about 10 vol% CO 2 ice is mixed within the polar deposits. This is the first time a large quantity of CO 2 ice is constrained to exist in the north polar cap. Like on Earth, where the composition of buried ices gives hints on the climatic evolution, having CO 2 ice at the north pole of Mars will help improve scenarios for the climate evolution of the planet. Key Points: Radar data and a flexural loading model are used to probe the composition of the north polar cap of Mars and the strength of the lithosphereThe elastic thickness beneath the north polar cap is found to be between 330 and 450 km, implying regional heat flows of 11 to 16 mW m −2For reasonable dust contents, large quantities of CO 2 ice must be mixed within the polar cap to be consistent with our inferred compositions [ABSTRACT FROM AUTHOR]