The range of zero pressure densities of the Martian mantle which are compatible with the mean density and moment of inertia factor of Mars has been explored by: a) considering the full range of plausible core compositions and densities, and b) investigating the sensitivity of computed mantle densities to uncertainties in the input parameters. Ni, Fe, Fe3O4, and FeS cores were considered; corresponding zero pressure mantle densities range from 3.47 to 3.41 g/cm3. Uncertainty in the mantle density of about 0.04 g/cm3 for the Fe core model and about 0.05 g/cm3 for the FeS core model results from uncertainties in the input parameters. The zero pressure density of the Martian mantle is estimated to be 3.44¿0.06 g/cm3.