The “Excavation and Mobility Modeling” task of the Johns Hopkins led “Scientific Exploration Potential of the Lunar Poles” NLSI project is to develop physically based discrete element method (DEM) models of the interaction of wheeled mobility platforms and excavation tools with lunar regolith at the poles and elsewhere. The DEM explicitly models the dynamics of assemblies of particles, such as regolith (the layer of loose rock particles covering bedrock). It is particularly useful when a material undergoes large-scale discontinuous deformations that depend on micro-scale contact processes, internal breakage of contact bonds, and compaction of broken fragments, such as occur during excavation and mobility processes. We have developed the COUPi (Controllable Objects Unbound Particles interaction) DEM and applied it to geotechnical problems of regolith settlement, geotechnical strength, and penetration mechanics. COUPi is currently being used to simulate wheel mobility conditions for the Mars Exploration Rover in support of a dynamic rover/regolith interaction model. COUPi can simulate inter-particle self-gravitation, to allow simulation of regolith on asteroids and asteroid mechanical processes. Complex particle shapes (Polyhedra) are used to simulate the effects of particle interlocking processes, which are important in regoliths. Comparison of DEM simulations using physical DEM capabilities, developed by the Cold Regions Research and Engineering Laboratory (CRREL), of wheel digging, static excavation, and dynamic excavation with experimental results demonstrate that DEM physical models more accurately represent physical conditions than DEM models using empirical parameters. Physical particle parameters include particle shape, size distribution, particle contact friction, particle solid density, regolith bulk density, modulus, and gravity. Consistent with experimental results, DEM simulations indicate that complex particle shapes improve the accuracy of wheel digging simulations (wheel torque and sinkage) compared to using spherical particle shapes and that percussive excavation greatly reduces the forces associated with excavation compared to quasi-static excavation. CRREL simulations of tool impacts in JSC-1a, using polyhedral particles, on a Cray XE6 has demonstrated a linear increase in computational speed with CPU number using up to 512 CPU’s, which is the most that have been used so far and indicates that further improvements in computational speed will be possible. We have also examined the effects of particle size distribution and density on regolith strength and the role that particle shape, contact friction and settlement processes play in controlling particle bed bulk densities. Future plans are to continue improving COUPi simulation capabilities by adding physical process algorithms to simulate volatile migration in regolith and regolith properties in low and variable gravity conditions (e.g., on small bodies). COUPi’s computational efficiency is constantly being improved through increased algorithmic efficiency and parallelization processes. COUPi can be used on a variety of multi-processor platforms including laptops, multiprocessor desktops, and supercomputers.