Mode-matching and beam-propagation methods are used to analyze single-mode operation of optical GeSi-Si and Si-SiO<sub>2</sub> semiconductor rib waveguides. The waveguide dimensions that allow only the fundamental HE<sub>00</sub> or EH<sub>00</sub> mode to propagate have been determined. For both material systems, it is found that the rib can be several microns wide and several microns high, thus allowing efficient coupling to single-mode fibers. Numerical examples are given for monomode guiding group-IV materials, but the results apply to III-V rib waveguides. It is shown that single-mode rib guides with large cross sections are feasible as long as the waveguide is at least several millimeters long