Granite formations have been frequently involved in subsurface energy‐related activities such as radioactive waste disposal, oil, and gas storage. This is principally because of their mechanical stability, low permeability, and high corrosion resistance. These favorable properties, however, can be compromised by the addition of mineral veins, which tend to occur ubiquitously in upper crustal rock formations. Evaluation of the impact of veins on the integrity and rupture characteristics of granite, especially under true triaxial stresses, is therefore important yet currently underemphasized. This study examines the rupture of veined granite in polyaxial compression via a discrete element method model. In the model with soft veins, the rupture is localized along the fabricated inclined veins (45° relative to the horizontal with strike running in the σ2 direction) under low confining stresses (σ2 < 67 MPa); in contrast, a combined rupture of veins and granite matrix is observed when σ2 is increased to 141.6 MPa. Shear sliding along the inclined veins is revealed by examining the displacement field. Shear‐induced volumetric dilation is suspected in the soft‐veined models in relatively low confining stresses (σ2 < 67 MPa) with sliding and dilation behavior apparently suppressed at σ2 = 141.6 MPa. Hard veins impede local rupture, resulting in conjugate shear bands. The well‐recognized σ2 effect is observed for the hard‐veined models, while no pronounced σ2 effect is noticed for the soft‐veined models. This study also reveals that vein thickness has a negligible impact on rupture characteristics, which is however profoundly affected by vein orientation.