Considering the influence of transverse shear deformation and large displacement, the basic non-linear dynamic equations of high pier under impulse loads are established for bi-linearity constitutive model. By supposing the displacement shape function and applying the Galerkin method, the dynamic motion equations about time are gained. The dynamic motion equations are resolved, the critical loads and displacement response curves are obtained, and the influence of the vary kinds of loads and the geometry parameters of high pier on the critical loads are analyzed. The loads-displacement curves under triangle impulse loads are compared with under rectangle impulse loads. The displacement response curves under impulse loads with different peak and the softness- critical loads curves under rectangle impulse loads are given. The influence of the different persist time of rectangle impulse loads on the critical loads is analyzed. The influence of the plastic deformation on stability of the high pier is analyzed. The process that the plastic range appeared and enlarged is provided.