The extended finite element method (XFEM) is presented to simulate natural fracture and hydraulic fracture. The generalized nodal shape functions are used in a cluster of nodes around cracks. To improve the accuracy in the vicinity of crack

a ramp function is used to avoid the blending element problem. An uncoupled model is used for hydraulic fracturing

which assumes uniform water pressures at crack faces. The mortar method (segment-segment contact approach) in combination with the augmented Lagrange’s method is adopted to establish contact conditions between the closed natural fracture faces. Several numerical examples are analyzed in detail. In comparisons with analytical solutions

the proposed method obtains higher accuracy on computing the stress intensity factors of the pressurized crack and the hydraulic fracture with the uniform water pressure on the crack faces. The influence of hydraulic fracturing on natural fracture face is simulated

and the contact stress and contact condition on the natural fracture face are further analyzed.