Fracture process is investigated using finite-difference simulations with a new constitutive model. It is shown that both geometry and fracture mechanism itself depend on the preexisting heterogeneities that are stress concentrators. In the brittle regime (low pressure, P), Mode-I fractures propagate normal to the least stress σ₃ from the imposed weak zones. At high P, shear deformation bands are formed oblique to σ₃. At intermediate values of P, the fracture process involves both shear banding and tensile cracking and results in the initiation and propagation of pure dilation bands. The propagating band tip undulates, reacting on the failure mechanism changes, but its global orientation is normal to σ₃. The σ₃-normal fractures are joints. There are thus two types of joints resulting from Mode-I cracking and dilation banding, respectively. The obtained numerical results are in good agreement with and explain the results from previous similar experimental study.