Radiation shielding analyses are performed for a candidate Mars base habitat. The Langley cosmic ray transport code and the Langley nucleon transport code are used to quantify the transport and attenuation of galactic cosmic rays and solar flare protons through both the Martian atmosphere and regolith shielding. Doses at the surface and at various altitudes were calculated in a previous study using both a high-density and a low-density Mars atmosphere model. This study extends the previous low-density results to include the further transport of the ionizing radiation that reaches the surface through additional shielding provided by Martian regolith. A four-compound regolith model, which includes SiO2, Fe2O3, MgO, and CaO, was selected based on the chemistry of the Viking 1 Lander site. The spectral fluxes of heavy charged particles and the corresponding dosimetric quantities are computed for a series of thicknesses in the shield media after traversing the atmosphere. These data are then used as input to algorithms for a specific shield geometry. The results are presented as the maximum dose received in the center of the habitat versus various shield thicknesses for a base at an altitude of 0 km and 8 km.