Based on the Hamilton formulation of electro-magnetic waveguides,a finite element semi-analytical transverse discretization with symplectic formulation is used to solve waveguides with complicated cross sections.The method is applicable to arbitrary an-isotropic materials and is easy to deal with interface conditions between different materials.It can be used to solve complicated problems difficult with analytical methods.The edge element is used in discretization.Rectangular waveguide,rectangular waveguide with T-septum and layered waveguide are studied.Numerical results approximate to theoretical results and do not show spurious solutions.