The nonlinear governing equations of dynamic post-buckling of cylindrical shells are obtained aid the energy method and Hamiltonian system. Based on eigensolutions of the linear pre-buckling of the shells in Hamiltonian system, the nonlinear post-buckling of the shells, which are impacted by radial pulse loads, is discussed. The problem is reduced to the expandedness of eigensolutions and the computation of recursion formulas. For computing, the mode of the pre-buckling is considered as the initial mode. The evolvement process of the post-buckling is revealed. The results show that the influences for the amplitude of the initial mode is less in some thickness of shells, whereas, the post-buckling behaviors of shells are sensitive to the thickness and the length of shells, the intension time of pulses.