Numerical methods have been used for the solution of electromagnetic problems for long years. The advancement of the computer technology has led the numerical methods to obtain a widespread usage. One of the most frequently used numerical methods in recent years is finite difference time domain method (FDTD). In this paper, the propagation of electromagnetic waves in a two dimensional plasma medium is investigated via finite difference time domain method. The behaviour of electromagnetic waves at the boundaries of the problem space has been studied by using PML and Mur type absorbing boundary conditions (ABC). In simulations, it is shown that PML type absorbing boundary condition gives better results than Mur type absorbing boundary condition.