In rock-type materials

two types of cracks are observed under combined compression and shear loading: the tensile wing cracks

and the frictional secondary cracks. On the basis of the extended finite element method (XFEM)

an extended finite element displacement enrichment method to model the interaction of the frictional crack surfaces is given. Besides

an approach to deal with the branched cracks is also presented. The maximum circumferential tensile stress criterion and the Mohr-Coulomb criterion are adopted respectively to predict the initiation and propagation of the tensile cracks and the frictional cracks. A Matlab program Betaxfem 2D has been developed and the proposed methods are verified through two examples; and then the crack bifurcation and propagation processes of the specimens with pre-existing closed fractures under uniaxial compression loading are simulated. The comparison with the experimental results indicates that methods proposed can be used to simulate and predict the initiation and propagation of the interactive tensile and frictional branched cracks in rock-type materials.