The stress intensity factor (SIF) of an arch door structure is a crucial parameter for characterizing the strength of stress field at the tip of a radial crack. However, calculating the SIF of an arch door structure under differential settlement remains challenging. In this paper, we derive an analytical formula for the SIF of an arch door's radial crack subjected to differential settlement. First, considering the arch door's symmetry, we decompose it into a superimposed form of positive and antisymmetric states, using the force method to analyze the internal force distribution within the structure. Next, we express the stress distribution along the thickness direction on the arch door's crack section using the section method, based on the internal force situation. Finally, we integrate the product of the weight function and the stress distribution on the crack surface using the weight function method, obtaining an analytical solution for the SIF of the arch door under differential settlement. Our analytical results align with the findings of ANSYS numerical simulations, demonstrating that both mode-I and mode-II SIF exhibit a significant linear response trend with respect to the differential settlement value and radial crack angle. These experimental results suggest that the analytical solution presented in this paper can accurately and effectively model the SIF of arch door cracks under differential settlement, providing valuable insights for crack propagation analysis.