A Monte Carlo model was developed to simulate multiple scattering and depolarization of LIDAR signals in water ice clouds and mineral dust in the atmosphere of Mars. This model was used to test the viability of an orbital LIDAR system for the study of the Martian atmosphere. It was found that a system with the same laser as the Earth-based CALIPSO orbital LIDAR system but with a receiver telescope with half the diameter of CALIPSO's is capable of producing reliable measurements of typical Martian cloud and dust conditions.