This talk summarizes an effort at the Modeling, Simulation and Visualization Center at the University of Wisconsin-Madison to model and simulate large scale discrete dynamics problems. This effort is motivation by a desire to address unsolved challenges posed by granular dynamics problems, mobility of tracked and wheeled vehicle on granular terrain, and digging into granular material, to name a few. In the context of simulating the dynamics of large systems of interacting rigid bodies, we briefly outline a method for solving large cone complementarity problems by means of a fixed-point iteration algorithm. The method is an extension of the Gauss-Jacobi algorithms with over-relaxation for symmetric convex complementarity problems. Convergent under fairly standard assumptions, the method is implemented in a scalable parallel computational framework by using a single instruction multiple data (SIMD) execution paradigm supported by the Compute Unified Device Architecture (CUDA) library for programming on the graphical processing unit (GPU). The simulation framework developed supports the analysis of problems with more than one million rigid bodies that interact through contact and friction forces, and whose dynamics are constrained by either unilateral or bilateral kinematic constraints. Simulation thus becomes a viable tool for investigating in the near future the dynamics of complex systems such as the Mars Rover operating on granular terrain, powder composites, and granular material flow. The talk concludes with a short summary of other applications that stand to benefit from the computational power available on today’s GPUs.