The interaction between hydraulic fractures and natural fractures have significant influence on the geometry of hydraulic fracture network in fractured reservoirs. However, in previous mathematical model, the coupling relationship of non-intersecting fractures in propagation process was often been ignored, which resulted the distortion of simulation results of fracture network. Based on boundary element method and rock failure criterion, we established mathematical model to study the fracture interaction mechanisms and fracture network morphology under induced stress. Realized the visualization of the global fractures coupling effect in simulation. Compared with epidemic perception, we put forward different understandings about the coalescence conditions and the intersection model under the interaction of fractures. In addition, proved the existence of stress shielding and transferring effect. The morphology and associated factors of complex fracture network were analyzed based on the mechanism of multi-fracture interference, which may be helpful to improve fracturing simulation model and increase fracturing effect.