Abstract: The complexity of a hydraulic fracture network depends on the behaviors of induced hydraulic fractures as they intersect natural fractures, so it is important to understand the mechanism of fracture intersection under particular field conditions of in-situ stresses, rock and natural fracture properties. An accurate criterion for the fracture propagation across natural fractures is established, and the direction of the reinitiated fracture is also studied. The results show that for a given approaching angle there exits a certain range of stress ration when crossing occurs, beyond this range crossing will not occur. Under high horizontal differential principle stress and approaching angle, hydraulic fracture is more likely to cross the natural fracture. As the stress ration increases, the direciton of reinitiated fracture draws closer to the direction of the incremental principle stress. This new criterion can be applied in the general analysis of fracture network and simulation of numerical fracture network.