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.