Abstract: It is necessary to accurately predict the fracture initiation pressure at different positions when a staged hydraulic jet fracturing program is designed and optimized. In this paper,therefore, a fracture initiation model which takes the induced stress field into consideration is established for the staged hydraulic jet fracturing on the basis of Westergaard theory. The effect of the induced stress of the first fracture on the following initiation fracture was investigated and compared with the actual fracturing data. In addition, an analysis was conducted to determine the effect of fracture height, net fracture pressure, minimum horizontal in-situ principal stress and fracture spacing from the first to the second one on the initiation pressure of the second fracture.The calculated results showed that the model calculations and the test values were maintained identical. In situations with practical parameters, the following initiation pressure increased by 3 MPa if the net pressure at the fracture plane increased by 5 MPa. It increased by 2 MPa, and the influential range of induced stress field enlarged by 30 m if the height of first fracture increased by 10 m. The following initiation pressure increased with the shortening of the spacing to the first fracture, with maximum increase ratio 21%. The minimum horizontal in-situ principal stress had no effect on the influential range of induced stress field. It was shown that the fracture initiation model established in this paper was better accordant with the field testing data. The following fracture initiation pressure was significantly affected by the net fracture pressure, the fracture height and the spacing to the first fracture, but was hardly affected by the minimum horizontal in-situ principal stress. The research results in this paper played an instructive role for the design and optimization of staged hydraulic jet fracturing programs.