Abstract: In order to solve electro-magnetic problems with complicated cross-sections, based on the Hamilton formulation for electro-magnetic wave-guides, the method of finite element semi-analytical transverse discretisation under symplectic geometric form is applied. This method can be used in arbitrary anisotropic materials, and is convenient for treating interface conditions between different materials. A 2-D example of symplectic semi-analytical method is given. The eigenvalue 2.437 58 μm^-1, which is very close to the analytical result 2.475 96μm^-1, shows that this method is effective.