The purpose of our study is on the dynamic instability, that is dynamic buckling, of structures such as elevated expressways, towers and high-storied building subjected to a horizontal and a vertical excitations simultaneously. The coupled motion of equation with a horizontal and a vertical excitations simultaneously for these structures is derived in this paper, and this modeling is shown to become a Mathieu type’s parametric excitatoin. The numerical simulation analysis is carried out for an elastic beam model with an attached mass on its tip instead of a shell model as a first step of our study. Comparing with the classical seismic analysis method, this proposed dynamic stability analysis method shows the larger deformation in horizontal direction due to the parametric excitation of a vertical seismic wave.

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