A 3D numerical model with strong discontinuities implemented within the Enhanced Finite Element Method (E-FEM) is developed to address multi-cracking problems. Two failure criteria are proposed for two (tensile and shear) fracture kinematics; namely an anisotropic Mohr–Coulomb criterion with sliding and an anisotropic principal strain criterion with pure opening. This model is used to reproduce induced fracture networks around drifts after an underground excavation. A transversely isotropic behaviour is considered for the host rock. The influence of the anisotropy of rock properties and the in situ stress field on the induced fractures and the convergence of drifts are also studied.