During hydraulic fracturing process of the Permian Basin in North America, the cluster spacing has been shortened to 3m, and stress shadow can no longer be ignored. Many scholars have studied the influence of stress shadows to optimize cluster spacing. For reservoirs with natural fractures, how to activate more natural fractures through hydraulic fracturing has become the purpose. However, few scholars have studied changes in the activation law of natural fractures under stress shadow conditions. This paper establishes stress change value around single fracture according to Sneddon formula, and calculates the maximum and minimum principal stress according to plane principal stress calculation formula. Considering attenuation of net pressure, stress field of multiple fractures is established, and influence of various factors on stress re-orientation is studied. Finally, considering attenuation of net pressure with distance, according to discriminant formulas of tension & shear activation, the proportion of natural fractures that are easily activated is calculated. By designing orthogonal experiments, the influence of different factors on the proportion of activated natural fractures was studied. The stress increase in the direction of the minimum principal stress is much greater than the increase in the direction of the maximum principal stress. The stress increases in the direction of the maximum principal stress at the tip of the hydraulic fracture. The tip position between hydraulic fractures is "neutralized" due to the superposition of shear stress. Stress-fracture angle and the in-situ stress difference are the common main influencing factors for both tensile and shear activation, but the net pressure has little effect on the tensile activation of natural fracture. The fracture spacing has little effect on the activation of natural fractures. When formulating the fracturing scheme, we should pay more attention to the net pressure rather than the fracture spacing. This article provides a fast calculation method for the activation state of natural fractures considering the stress shadow, which provides a reference index for activating more natural fractures and increasing the production of a single well.