The study on induced stress of hydraulic fracturing is an important part of hydraulic fracturing design, temporary plugging and steering fracturing design, and completion design in oil and gas development. Based on fracture continuum method (FCM), cohesive unit method, and finite volume method (FVM), the propagation behavior of multiple hydraulic fractures (HFs) in fractured‐porous media reservoir is simulated from the perspective of fluid and geological stress coupling. The influence of natural fractures (NFs) on stress distribution and stress inversion sensitive factors are studied. NFs in the model are equivalent to physical models controlled by tension and shear bonds. The proposed model can deal with any number of NFs, which greatly improves the computational efficiency of the model. Then PKN analytic solution and Abaqus software results were used to verify the correctness of our model. The results show that the NF will make the reservoir stress show strong heterogeneity after fracturing, and the prominent feature is the regional stress mutation. The sudden change of stress shows the sudden increase or decrease in stress; with the increase in the initial stress difference, the stress inversion becomes more difficult. When the stress difference exceeds 3 MPa, the stress inversion area is almost 0. The stress interference increases with the decrease in cluster spacing. The stress inversion region between HFs decreases, while the external stress inversion region increases; Biot coefficient has great influence on stress and stress inversion. With the decrease in Biot coefficient, stress inversion region will decrease obviously. When the Biot coefficient is 0.4, there is no stress inversion area in the whole reservoir. Poisson's ratio has little influence on stress inversion. When Poisson's ratio changes between 0.1 and 0.3, the change range of stress is within 1 MPa, and the stress inversion area is almost unchanged. Our results can be helpful for understanding the stress distribution after hydraulic fracturing in fractured‐porous media.