We formulated an efficient numerical method for the dispersion relation of polaritonic channel waveguides and applied it to ZnO (wurzite) and ZnSe (zinc-blende) waveguides. The dispersion relation obtained by our calculations is distinct from that of bulk crystals. We found that important contributions to light propagation were made by two modes in the frequency range below the transverse exciton frequency, which was confirmed by comparing the group index obtained by our calculation with Fabry-Perot interference experiments. The numerical error of our method was estimated to be less than 1 % by comparing it with an analytical solution for a model structure. Our calculations predict an extremely small bending loss, which was estimated from the spatial decay rate of evanescent waves outside of the waveguide.