Abstract: Based on the Hamilton formulation for electro-magnetic wave guides, the finite element semi-analytical transverse discretization under the symplectic formulation is used to solve the problems of wave guide with complicated cross sections. This method can be applied to an-isotropic materials, easier for treating interface conditions between different materials. The symplectic structure should be kept unchanged for various interface conditions. Examples of rectangular wave guide, rectangular waveguide with T-septum, layered waveguide, anisotropic waveguide are presented. The numerical results approach the theoretical results.