The phenomenology of shock loading effects in brittle mass has been of interest to researchers and engineers. The shock loading as blasting causes strong stress waves in the structures. Discontinuous faces due to shock waves interrupt the tensile stress wave propagation and reflect the stress wave propagation. To predict the fracturing behavior of brittle mass, it is required for the numerical method that can analyze the colliding and slipping behavior of discontinuous faces and the wave propagation in the mass, simultaneously In this study, the wave propagation in the brittle materials is analyzed using the modified distinct element method to be able to predict the behavior of discontinuous structures. The behavior of an unsupported bar subjected to loading at the end is analyzed to verify the rigid body motion of a bar and the relative displacement in the bar. The colliding behavior of two bars is analyzed to investigate the propagation of stress waves in the bar. The fracturing behavior of a bar due to impact loading is analyzed to investigate the propagation of stress waves in the bar with and without the discontinuous faces. The applicability of the modified distinct element method to the wave propagation problems is investigated.