Hydraulic fracturing is recognized as the main stimulating technique to enhance recovery in tight fissured reservoirs. These fracturing treatments are often mapped by use of hypocenters of induced microseismic events. In some cases, the microseismic mapping shows asymmetry of the induced-fracture geometry with respect to the injection well. In addition, the conventional theories predict fracture propagation along a path normal to the least compressive in-situ stresses, whereas in some cases the microseismic data suggest fracture propagation parallel to the minimum compressive stress. In this paper, we present an extended-finite-element-method (XFEM) model that can simulate asymmetric fracture-wing development as well as diversion of the fracture path along natural fractures. Simulation results demonstrate the sensitivity of the fracture-pattern geometry to differential stress and natural-fracture orientation with respect to the in-situ maximum compressive stress. We examine the properties of sealed natural fractures that are common in formations such as the Barnett shale and show that they may still serve as weak paths for hydraulic-fracture beginning and/or diversion. The presented model predicts faster fracture propagation in formations where natural fractures are favorably aligned with the tectonic stresses.