4H-SiC Photoconductive Semiconductor Switches (PCSSs) have shown significant promise for use in pulsed power related switch applications. This simulation uses the finite difference method, parallelized using a NVIDIA graphical processing unit and the CUDA framework, to solve the system of partial differential equations that model the semiconductor physics involved in the high voltage blocking state of the photoconductive switch. By taking into consideration material properties (mid-band gap trap energy level and concentration, etc.), we are able to gain an understanding of how changes in these parameters affect the space-charge-limited (SCL) currents observed in the high voltage blocking state. This subsequently allows for a fundamental understanding of the parameters controlling the high voltage switching capability of photoconductive switches. Results of the simulation are presented.