A calculation model for stress field due to horizontal well staged fracturing is proposed according to stress superposition principle. The model considers the influence of the wellbore pressure, in-situ stress, fracturing fluid seepage, thermal stress, perforation and artificial cracks. It can accurately adapt to the change of stress field around the wellbore in the process of staged fracturing in horizontal wells, and guide the research of the fracture initiation and extension mechanism. The model focuses on the induced stress caused by artificial cracks in the plane around the horizontal wellbore with the method of the displacement discontinuity. The model can also overcome the limitation of ordinary induced stress analytical models which can only calculate the induced stress in the fracture height plane. Results show that the fracture pressure calculated with the proposed model is consistent with the actual fracture pressure, which demonstrates the accuracy of the model. The artificial fractures can cause great impact on stress field around the wellbore. The stress concentration at the crack tips can result in the reduction of stress components and the obvious increasing of the stress components around a given area of fractures. Meanwhile, the more artificial fractures are fractured, the more serious the stress interference is and the more complex the stress distribution around wellbore is. The research has significance in analyzing the crack initiation and propagation mechanism under the influence of crack interference and provides guidance to fracturing design as well.