Cavity expansion within soil or rock is an important issue in geomechanics because it often appears in geotechnical related problems. This work describes the initiation of fracture in a laboratory specimen of Berea sandstone with a cylindrical opening, modeled using the discrete element method (DEM). The effect of far-field stress and borehole size on breakdown (peak) pressure was investigated. The results demonstrated that an increase in either the far-field stress or the borehole diameter caused the peak pressure to decrease. This showed that the size effect was governed in part by both the loading conditions and borehole size.