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In view of fluid flow in cracks and rock deformation, the mathematical model for shale hydraulic crack propagation was established. The crack flow field and the rock stress field were solved with the finite element method and the extended finite element method respectively, and the two fields were coupled through the Picard iteration. The presented model gave results consistent with those of the classic model, which verified correctness of the former. Based on the model, the effects of the rock elasticity modulus, Poisson's ratio and injection rate on the crack geometry, and the dynamic process of a hydraulic crack approaching a natural crack at an arbitrary angle, were simulated. The numerical results show that the elasticity modulus and injection rate have significant influence on the crack geometry, while the Poisson's ratio has little effect; the more brittle the shale is, the longer and narrower the hydraulic crack will grow; the greater the principal stress difference and the approaching angle are, the easier the hydraulic crack crosses the natural crack; there is a relatively large decrease in the crack width at the intersection between a hydraulic crack and a natural crack; the extended finite element method avoids mesh reconstruction and refinement during computation, and reduces the computing time. The presented model provides an effective theoretical tool for the shale fracturing design. [ABSTRACT FROM AUTHOR]