The study of the stress intensity factor at the crack tip under the interaction of multiple stress fields is an important part of fracture mechanics, the understanding of which is critical to the fracture criterion and strength analysis of compressed materials. On the basis of the initial solution of uniaxial compression of circular hole plate, the crack tip stress intensity factor integral equation of circular hole plate under uniaxial compression is derived by superposition principle, and the approximate solution of the integral equation is derived by Chebyshev polynomial. Then, the same problem is analyzed by finite element method, and the solution is compared with the approximate solution of the integral equation. Meanwhile, the effects of circular hole size, crack size, crack location and crack surface friction coefficient on the stress intensity factor at the crack tip are analyzed. The results show that the solution of the stress intensity factor at the crack tip obtained by the superposition principle is basically consistent with that of the finite element method, so the integral equation based on the initial solution and the superposition principle is proven correct. Larger crack size and circular hole size, closer to the hole edge and smaller crack surface friction coefficient all lead to greater stress intensity factors. Furthermore, the fluctuation of the crack stress intensity factor close to the hole edge is more obvious than that far away from the hole edge.