This paper is concerned with an numerical analysis of electromagnetic wave propagation from randomly rough surfaces as a desert, sea surface and so on. We propose discrete ray tracing method (DRTM) for analysis of characteristics of wave propagation along one dimensional (1D) and two dimensional (2D) random rough surfaces. The point of the present method is to discretize not only rough surface but also ray tracing. This technique helps saving computer memories and does simplifying ray searching algorithm resulting in saving computation time. Numerical calculations are carried out for 1D and 2D random rough surfaces and electric field distributions are shown to check the effectiveness of the proposed DRTM.