Abstract: The initiation, propagation and coalescence of cracks during rock failure are always in three-dimensional distribution, so the three-dimensional simulation would be more helpful in capturing the three-dimensional failure process of rock. In this paper, firstly, under the parallel computing environment in Northeastern University of China, a numerical code capable for simulating three-dimensional failure process of rock, RFPA^3D-Parallel code, is used to simulate the failure process of rock specimen with a pre-existing circular opening under uniaxial, biaxial and triaxial loading conditions. The numerical simulations indicate that: (1) the cracking patterns around the opening under uniaxial compression are well predicted, validating the capability of RFPA^3D-Parallel in simulating the cracking zone around the opening; (2) under the biaxial compression the failure surface parallel to the loading plane is observed; (3) the complex failure patterns under the combination of triaxial loading conditions are numerically simulated, and the zonal disintegration around the opening can be captured when the rock specimen is highly compressed in the direction of the axis of hole and is confined in other two directions.