Abstract: For rock specimens with initially random material imperfections in uniaxial plane strain compression, the effects of initial cohesion and internal friction angle on the failure processes were modeled using FLAC. FISH functions were used to generate random imperfections and to remember the number of failed elements. For the intact rock exhibiting the linear strain-softening behavior beyond the occurrence of failure and then the ideal plastic behavior, the failure criterion is a composite Mohr-Coulomb criterion with tension cut-off. The imperfection undergoes the ideal plastic behavior beyond the occurrence of failure. As the strength parameters (initial cohesion and internal friction angle) increase, the stress drop and incremental axial strain from the peak stress to the residual stress increase; the occurrence of shear fractures intersecting the specimen is later and the final number of yielded elements decreases. For the intact rock with higher strength parameters, after all imperfections fail it does not fail immediately; instead, when the axial stress reaches a certain value it starts to yield and the increase in the number of failed elements is less apparent beyond the peak stress. In the loading process, the acoustic emissions are apparent in three stages. The first stage, the second stage and a majority of the third stage appear at pre-peak. Prior to the peak stress and in the third stage, the increase in the acoustic emissions results from the extension, coalescence and propagation of imperfections and the competition among imperfections. Higher strength parameters of the intact rock cause the third stage to be wider and the number of acoustic emissions to be lower, suggesting that the failure is more progressive and the failure duration is longer.