A two-phase model of rock was proposed in order to investigate the mechanism of brittle fracture due to uniaxial compression, in which rock was considered to be a composite material consisting of hard grains and colloids. The stress state in colloid region near grains was calculated using Finite Element Metnod ( FEM). The influence of the tensile stresses on the crack initiation and failure process of brittle rock subjected to uniaxial compression was investigated by numerical experiments. The FE results show that tensile stresses are induced easily in the neighboring area of hard grains with the maximum value near grain boundaries. The distribution of tensile stresses depends on the relative position of hard grains. The cracks initiated just near the boundary area of hare grains, which was goved by tensile stress. These results dearly reveal the micro-fracture mechanism of brittle rock loaded by uniaxial compression. It can be concluded that the failure mode of brittle rock under uniaxial compression is still tensile fracture from the point view of microstructure. However,since the wide colloid region is still under compressive stress state, further propagation of boundary, cracks through this region obviously needs more extal load, thus causing the uniaxial compressive strength of rock much higher than its tensile strength obtained via Brazilian (splitting) experiment.