In this work, a hybrid discrete-continuum numerical model was used to simulate hydraulic fracture (HF) crossing and interaction with natural fractures or weakness planes. The model provided unique capabilities for investigating effects which have usually been overlooked or not able to be modeled in many of the previous studies on the subject. Multiple effects, such as the influence of stress conditions, material in-homogeneity (stiffness and strength contrast), natural fracture properties (crossing angle and friction angle), and injection parameters (injection rate and fluid viscosity) were investigated in this new work. Three types of intersection between an HF and orthogonally aligned natural fractures were identified by varying the coefficient of friction of the natural fractures and the stress ratio. In addition, the intersection angle between an HF and natural fractures or weakness planes was found to significantly affect the crossing. Decreasing the intersection angle with the natural fractures impeded direct crossing and favored the arrest of an HF. Material in-homogeneity and injection parameters were found to also greatly affect the HF crossing of natural fractures. Ultimately, the simulations showed that the geometry of an HF can be greatly affected by the interactions with adjacent natural fractures and weakness planes and that complex HF propagation patterns will occur due to complicated crossing behavior during hydraulic fracturing in naturally fractured reservoir systems.