A hybrid scheme that incorporates the method of finite elements, he method of lines, variational techniques, and conformal mapping is proposed for the analysis of guided-wave structures. This technique is devised to analyze complex waveguide structures with irregular composite geometries.High numerical accuracy is maintained by treating key singularities by semianalytical procedures. Compared with the conventional method of lines with finite difference techniques, the proposed scheme is able to solve many complex guided-wave problems with fewer mesh lines without compromise on accuracy. This gain is due to the added variable mesh-directions and the flexibility in the method of finite elements in choosing appropriate functions for fitting the configuration of concern.