A contact model for rock is established and imbedded into a DEM software by summarizing the bond granule tests. DEM simulation of uniaxial compression test on the pre-cracked Lac du Bonnet granite is performed, and then stress distributions are further analyzed and compared with the theoretical results. Different fracture criteria are employed to predict the crack initiation angles that are compared with theoretical ones. The results show that the failure modes obtained from DEM simulation are similar to experimental results, and stress distributions in DEM simulation are qualitatively similar to theoretical values. When the angle of pre-crack is small, the lateral stresses are compressive and tensile. The compressive strains concentrate at two edges, resulting in the tensile strains in the up- and downward cracks. When the angle of the pre-crack is large enough, the stress concentration is unobvious, leading to a discrepancy between the DEM and theoretical results. The crack extension angle resulting from uniaxial compression measured from DEM tests are in good agreement with those acquired from experimental tests. These angles are consistent with theoretical predictions by the maximum circumferential stress criterion and the maximum energy release rate criterion.