Abstract: Currently, there is limited research on the dynamic response of cross-sectional irregular piles, with the focus of vertical dynamic load studies primarily on circular piles. In light of this research gap, the governing equations and boundary conditions for the irregular pile-viscoelastic soil model were derived based on Hamilton's principle and variational calculus in a Cartesian coordinate system. A two-dimensional model of the irregular pile-soil system was established using COMSOL to solve the governing equations for the soil, overcoming the challenge of solving complex boundary condition control equations. The pile's governing equations were solved using MATLAB, and the coupled pile-soil control equations were iteratively calculated using MATLAB. A theoretical model capable of analyzing the dynamic response of irregular piles under vertical dynamic loads was developed. The computational results of this theoretical model were compared and validated against existing calculations for circular piles, confirming the reliability of the proposed method. The paper concludes with a discussion on the impact of pile cross-sectional parameters, the ratio of elastic moduli between the pile and the soil, and the slenderness ratio of the pile on the dynamic impedance at the pile head. The results indicate that：The impact of the cross-sectional shape effect on the pile-head impedance amplifies with the rise in frequency. Particularly, the distinctive shape effect is more pronounced in H-shaped piles compared to X-shaped and rectangular piles as the frequency escalates.