Rock is a typical non-homogeneous material. The behavior of a rock block under compression and the process of micro-fracture in that block are phenomena of considerable interest in understanding the strength characterization of brittle rock. In this study, the effect of the non-homogeneity on limit bearing capacity of rock block based on Rock Elasto-Plastic Failure Process Analysis code (REPFPA) are simulated and investigated. Numerical simulations find out that there exists a functional relation between the heterogeneity coefficient and the limit bearing capacity of rock block. For specimens with the same heterogeneity, however, the numerical simulations show that the failure modes depend greatly on the crack initiation location, which is found to be sensitive to the local disorder features within the specimen. In addition, the characteristics of acoustic emissions with the changing of heterogeneity coefficient were also found. These identifications are crucial for better understanding and interpreting the experimental results and consequently, improve our concepts in design or analysis of rock engineering structures.