This study treats the dynamic stability of mechanical systems subjected to multi-directional excitations, such as dynamic buckling behavior, etc.. A steel cylindrical pier is treated and modeled analytically as a thin cylindrical structure with an attached mass on its tip. The analysis is carried out by numerical simulations, where the horizontal and the vertical seismic loads are applied simultaneously. From the previous study, it is known that the seismic responses of the thin cylindrical shell structure tend to increase due to the coupling effects between the horizontal and vertical excitations, and that flattening phenomena occurs. In this study, the deformation behavior is investigated for very large external force.