In this article, the elastic buckling behavior of cylindrical shells under external pressure is studied by using a symplectic method. Based on Donnell's shell theory, the governing equations which are expressed in stress function and radial displacement are re-arranged into the Hamiltonian canonical equations. The critical loads and buckling modes are reduced to solving for symplectic eigenvalues and eigenvectors. The buckling solutions are mainly grouped into four categories according to the natures of the buckling modes. The effects of geometrical parameters and boundary conditions on the buckling loads and modes are examined in detail.