Abstract: Waveguide discontinuity problems are treated as three substructures which are homogeneous in the longitudinal direction.Transverse section is discretized by edge element.The export stiff matrices can be calculated by the precision integration based on Riccati equations in Hamilton system.The whole waveguide discontinuity problems can be solved by a combination of substructures.This method can deduce the dimension of the equations only because of transverse discretization.The calculation is independent of the increment of the longitudinal length because of precise integration. Thus the longitudinal length can be long enough to assure precision.