The cracked Brazilian disc (CBD) specimen is widely used in order to determine mode-I/II and mixed-mode fracture toughness of a rock medium. In this study, the stress intensity factor (SIF) on the crack-tip in this specimen is calculated for various geometrical crack conditions using the extended-finite element method (X-FEM). This method is based upon the finite element method (FEM). In this method, the crack is modeled independently from the mesh. The results obtained show that the dimensionless SIFs for the pure modes I and II increase with increase in the crack length but the angle in which pure mode-II occurs decreases. For the mixed-mode loading, with increase in the crack angle, NI value decreases, while NII value increases to a maximum value and then decreases. The results obtained from the crack propagation examinations show that the crack angle has an important effect on the crack initiation angle. The crack initiation angle increases with increase in the crack angle. When the crack angle is zero, then the crack is propagated along its initial direction, whereas in the mixed-mode cases, the crack deviates from the initial direction, and propagates in a direction (approximately) parallel to the direction of maximum compressive load.