At present, when using the improved dynamic Winkler model to analyze the stress conditions of foundation pit piles from earthquake shock, the reflection effect of the stress wave cannot be prevented, which renders the analysis result noncomprehensive and inaccurate. In this paper, we propose a stress analysis model for foundation pit piles subjected to seismic impact. We use a small strain model for foundation pit piles to describe the modulus change of the pile under different stress states, and use the finite element numerical simulation method to establish a finite element model for foundation pit piles in combination with the small strain model. When setting the boundary condition constraints of the finite element model for foundation pit piles, we choose an absorbent boundary of viscous dampers to prevent the refraction of the stress wave on the model boundary, and thereby avoid calculation error. We use the Newmark method to analyze the dynamic time history of the finite element model and determine the stress of foundation pit piles under different stress states. The experimental results show that the proposed model can effectively and accurately analyze the stress distributions of foundation pits and the bending moments and deformation displacements of the piles.