Numerical simulation of lunar regolith and simulant is of significant interest given the planned effort to establish a long term presence on the Moon. The granular behavior of these materials requires the representation of discrete particle interaction which is angular in shape. This paper describes Discrete Element Method (DEM) simulations with polyhedral particle shapes to reproduce recently conducted experiments on JSC-1A, a lunar soil simulant. In order to account for the highly angular JSC-1A particle shapes, a new DEM element library was developed from scanning electron microscope photos of JSC-1A particle. DEM model parameters were developed from available geotechnical properties, such as grain size distribution, or calibrated using selected experiments, such as contact damping ratio. The paper will discuss in detail the modeling approach and the results of a suite of simulations intended to reproduce experimental observations. The small particle size in the JSC-1A experiments would require the use of very large number of particles in the DEM simulations which is computationally very costly. Therefore, larger particle sizes have been employed while maintaining the general character of the grain size distribution curve. The simulation results show an overall good agreement with the experimental measurements, although limited stick-slip fluctuations in the force measurements are observed due to the larger size of particles in DEM simulations.