This dissertation is concerned with numerical simulation and study of the multiple steady states for a three junction semiconductor device. The semiconductor device is modeled by the drift-diffusion equations formulated by Van Roosbroeck. These nonlinear differential equations, the Poisson equation, two continuity equations and two current equations, describe the potential distribution, carrier concentration, and current flow within semiconductor devices;The system of semiconductor device equations can not be solved explicitly in general. The finite difference box method is used to transform the continuous equations into nonlinear algebraic system. The solutions are computed by two iterative schemes: Gummel's method and Newton's method;The basic goal in this dissertation is numerical simulation of one-dimensional steady state thyristors. A thyristor is a semiconductor device with four layer structure, used to control the switching of dc and ac power. Numerical simulation of thyristors is quite difficult because they have multiple steady states. The snap-back phenomenon in the current-voltage characteristic of thyristors has caused computational problems. We applied the arc-length continuation method to overcome the snap-back and multi-solution problems. We successfully obtain the current-voltage characteristic of thyristors by this method.