The transverse operator method is described for the study of different kinds of dielectric waveguides. The longitudinal section electric (LSE) modes and longitudinal section magnetic (LSM) modes of a corresponding dielectric stratified waveguide, also known as TE-to-xand TM-to-xmodes, have been chosen as the basis eigenfunctions, allowing rapid numerical convergence. The dispersion characteristics of some multidielectric waveguide structures have been obtained, as well as their attenuation constants. The results are compared to those previously published or measured and show good agreement. This formulation can be applied to other multidielectric structures with no modification.