In the near future, several exploratory missions to Mars are planned, which will include orbital radar sounders capable of characterizing the planet's subsurface structure to depths of up to a few kilometers. Due to the limited amount of resources concerning the properties of the Martian soils, in particular, those governing electromagnetic propagation and scattering, the ability of a radar system to detect and distinguish between subsurface interfaces is difficult to predict. Up to this time, most radar sounding simulations have been based on simplified models and do not accurately account for many of the factors that influence the response. To aid in the system evaluation and data interpretation for these missions, we developed a radar simulator to accurately model the response for various geological conditions. The simulator uses a frequency domain algorithm and is capable of modeling the effects of dielectric layering, volume debris, frequency dispersion, ohmic losses, and interface roughness. In this paper a geophysical model appropriate to the radar simulator is described, and the simulation algorithms are presented in detail. Factors influencing wave propagation and scattering are identified, including those that directly impact radar performance, specifically pertaining to expected penetration depths and unambiguous detection of water or ice. Finally, using a set of standard crustal models of different geological regions, simulation results are generated and presented.