Numerical modeling methods, such as the discrete element method (DEM), are an increasingly popular alternative to traditional semi-empirical terramechanics techniques. While DEM has many advantages, including the ability to model more complex running gear and terrain profiles, it has not reached widespread popularity due to its high computation costs. In this study a surrogate DEM model (S-DEM) was developed to maintain the simulation accuracy and capabilities of DEM with reduced computation costs. This marks one of the first surrogate models developed for DEM, and the first known model developed for terramechanics. By storing wheel-soil interaction forces and soil velocities extracted from constant velocity DEM simulations, S-DEM can quickly perform new dynamic wheel locomotion simulations. Using both DEM and S-DEM, wheel locomotion simulations were performed on flat and rough terrain. S-DEM was found to reproduce drawbar pull and driving torque well in both cases, though wheel sinkage errors were significant at times. Computation costs were reduced by three orders of magnitude in comparison to DEM, bringing the benefits of DEM modeling to vehicle design and control. The techniques used to develop S-DEM may be applicable to other common DEM applications, such as soil drilling, excavating, and plowing.