This report summarizes the result of the research carried out for the Postdoctoral Task E-6-7108 administered by the University of Dayton under contract F30602-81-C-0206 with RADC. The primary objectives of this research program were to learn whether there exists a dielectric waveguide configuration which offers lower loss figure than a circular dielectric rod and to establish an experimental technique to measure the guiding characteristics of waves on dielectric structures. These objectives were met. Future research areas are also described in this report. Keywords: Dielectric waveguides, and Millimeter waves.