Abstract: Shale gas deposits in shale reservoirs, whose bedding structures are different from conventional heterogeneous reservoirs. This also makes the shale reservoirs have different crack propagation laws in hydraulic fracturing. In order to investigate the crack propagation laws of shale reservoir hydraulic fracturing, complex variable function and conformal transformation is adopted here to deduce the solutions of crack tip stress concentration. The fracture propagation criterions have been put forward when the perpendicular to the minimum in-situ stress hydraulic fracture meets oblique bedding by considering shale reservoirs heterogeneity as well as strength anisotropy and then comparing fluid pressure satisfied fracture propagation in all directions. In order to show how difficult the hydraulic fracture turning to bedding, the critical strength ratios of bedding and rock mass are defined respectively when the fracture just initiates in bedding and propagates along bedding. Based on these two critical strength ratios, the bedding strength range which fracture initiates in bedding and propagates along bedding can be obtained. Analytical analysis show as follows:the critical strength ratio of bedding crack initiation increases with the decrease of bedding strike angle and dip angle and the increase of min-principal stress and the rock strength. The critical strength ratio of bedding crack initiation increases when the max-principal stress decreases and the middle-principal stress increase if the strike angle is less than 35.26°. Otherwise the critical strength ratio of bedding crack initiation decreases when the max-principal stress decreases and the middle-principal stress increase if the strike angle is greater than 35.26°. The critical strength ratio of bedding crack propagation increases when bedding strike angle, dip angle and in-situ stress difference decrease and the rock strength increase. Only when the critical conditions of bedding crack initiation and propagation all are satisfied do the hydraulic fractures turn to bedding.