Abstract: In this paper, the dynamic buckling of elasticcylindrical shells, which are impacted by axial load on one end, is studied.By introducing Hamiltonian system to the problem, critical loads andbuckling modes are reduced to the problems of eigenvalues andeigensolutions, respectively. In the system, symplectic eigensolutions aregrouped into two classes: the local compressive buckling and global flexurebuckling. Especially, when the impacted boundary is free, buckling modeshave special forms. Numerical results show some rules about the curves ofcritical load and corresponding buckling modes.