In this paper, the dynamic buckling of elastic cylindrical shells, which are impacted by axial step loads on one end, is theoretical analyzed in Hamiltonian system. A approach is employed to convert fundamental control equations into Hamiltonian canonical equations, which is shown in dual variables. In the system, critical loads and buckling modes are reduced to a problem of symplectic eigenvalues and eigensolutions. The primary factors, including impact time, boundary conditions, thickness and inertia force, etc，that affect critical loads and the corresponding buckling modes are investigated in detail. It is shown that buckling waveforms can be divided into two sorts according to different solving domains. The minimum critical loads belonging to different sorts have also an obvious discrepancy. The results give analytically and numerically some new rules of buckling problem, which is useful in designing structures of shells.