Abstract: Due to development of a large number of natural fractures in unconventional gas and oil reservoirs, the fracture expansion patterns during hydraulic fracturing are complicated. It is crucial to clarify the intersecting and expanding mechanical mechanisms among hydraulic fractures and natural fractures in three-dimensional space to predict the fracture patterns and fracturing stimulation effects. Aiming at the prediction of fractures extension patterns after the intersection of hydraulic fracture and natural fracture, based on force analysis for hydraulic and natural fractures in three-dimensional space, considering geo-stress field, induced stress field at the tip of hydraulic fractures and fluid pressure, and taking the hydraulic fracture penetrates or slides along the surface of natural cracks as the criterion, a mechanical model was established for fracture propagation accounting for the intersection of natural and hydraulic fractures. The modeling results show that: fracture propagation is affected by the joint effects of horizontal stress difference and the approaching angle, under the condition of high stress difference and large approaching angle, a simple penetrating fracture is tended to form, while with a small approaching angle natural fractures tend to sliding extension. When the inclination angle of natural fracture is large, it is easier for the hydraulic fractures to penetrate through the natural fractures then slipping propagate along the natural fractures, and when the inclination is small, hydraulic fracture is more inclined to remain do not penetrate the natural fracture. The slipping propagation for natural fracture is significantly affected by the injection rate of fracturing fluid. When the fluid pressure of fracturing grows, the positive stress at the natural fracture surface decreases correspondingly, which is more likely to induce a slipping propagation for natural fracture. The new model of intersecting extension of three-dimensional space hydraulic fracture and natural fracture established not only considers the influence of fracturing fluid pressure, but also analyzes the possible spatial slip extension of natural fracture, and the research results make up for the inadequacy of the existing theoretical methods of intersecting extension of three-dimensional space natural fracture and hydraulic fracture well.