Abstract: To recognize the three-dimensional near-wellbore propagation of hydraulic fracture, XSite, a simulator developed based on the lattice method and the synthetic rock mass, is used to analyze the influences of borehole orientation and in-situ stress on the propagation of hydraulic fracture. The results show that the variation of borehole orientation leads to the difference of fracture geometry, and the fracture tends to propagate along the plane perpendicular to the minimum principal stress. The increase of the intermediate principal stress will restrain the propagation of fracture perpendicular to this direction, and the hydraulic fracture parallel to this direction becomes straighter. Under a low stress ratio (ratio of the maximum to the minimum principal stresses), multiple fracture branches are induced on the borehole and tend to form a spatial fracture network. The increase in stress ratio will inhibit fracture branching. Under the high stress ratio, fractures tend to propagate along the direction of the maximum principal stress. As the fluid injects into the notch, the fracture will gradually deflect to the plane perpendicular to the minimum principal stress after propagating along the direction of the notch. There are no branches of the fracture that can be observed. The initiation mode does not change the dominating propagation direction of the fracture, but the stress field controls the propagation direction of the hydraulic fracture. The research results can provide references for the design and operation of hydraulic fracture.