We report the progress on a new computational technique for fully three-dimensional simulation of propagation of hydraulic fractures in the vicinity of a wellbore. One of the components of this technique is the boundary element code for modeling the elastic deformation of rock containing pressurized cracks developed previously by the first Author (see Nikolskiy, Mogilevskaya & Labuz, 2015). This code requires the use of only surface mesh, which facilitates its coupling with models of the fluid flow through the fractures. The code also features second order polynomial approximations of the boundary unknowns, which allow for accurate resolution of the cracks opening and sliding displacement near the tips and the stresses around these tips. In the present work, we further develop the code incorporating a fracture propagation algorithm that is capable of capturing the effects of mixed-mode loading (see Lazarus et al., 2001; Pham & Ravi-Chandar, 2016). In particular, we focus on the segmentation of the fracture front observed under combined opening (mode I) and anti-plane shear (mode III) load during fracture re-orientation from a wellbore. We discuss the importance of such fracture segmentation for the stimulation of unconventional reservoirs as well as for enhanced geothermal systems.