In this paper, based on the principle of superposition of acting forces, we propose a mathematical model for injected fluid-induced stress and calculate the stress distribution and SRV width vs. the stress difference in the formation. The results show that the nature of the propagation of the fracture network in multi-staged hydraulic fracturing depends on the stress in the initial cycle. The larger the horizontal stress difference, the larger the width of the fracture network in the rock. If the stress difference is greater than 5 MPa, the width of the fracture network decreases dramatically. When the net pressure is greater than 8 MPa, the width slowly increases. The calculation results are in good agreement with microseismic monitoring data for conditions in the Southwest shale field (China), suggesting that the proposed model is sufficiently reliable and accurate.