Uni-axial compression test has been the general way to evaluate the strength of bulk materials, especially brittle materials, for decades. In the field of concrete or rock mechanics, compression strength is one of the most significant engineering characteristics. By observing the compression test of a cubic specimen, the most severe compression area in material (the inner central area), however, does not match the damage pattern (side wedge peeling). In the present study, the Discrete Element Method (so-called DEM or Particle Element Method) is employed to analyse a brittle block. One of the important advantages of this method is that material damage due to bonding and friction failure can be better described. In this paper, the results of elasticity, compression strength, and the crack profile of the bulk specimen are carried out using the two-dimensional discrete element method. Upon matching the numerical results to those of the lab test, one can determine the internal material parameters such as bonding strength, the frictional angle, and equivalent stiffness between particles in micro scale.