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The purpose of this work was to study the rectangular dielectric waveguide and its transitions to metalwaveguide at millimeter wavelengths. The thesis reviews different dielectric waveguiding structures, theiranalysis methods and their transitions to the metal waveguide. In this thesis work the analysis methods andtransitions are further developed. The main results of this work are:1. It was shown that, after modifications, the Marcatili and Goell methods can be applied for calculatingpropagation constants of rectangular dielectric waveguide made of uniaxial anisotropic material with the opticalaxis oriented along the dielectric waveguide.2. Several tapering shapes were studied. It was shown that symmetrical E-tapering gives lower insertion lossesand smaller reflections compared with the H-tapering.3. Different cross-sections and geometry of tapering were studied using Agilent HFSS program. The mostappropriate dimensions were found.4. In the case of unsymmetrical tapering it was shown that better results are achieved when the axes of metal anddielectric waveguides do not coincide but differ by half of the tapering angle.5. Low insertion loss and small reflections were obtained with sapphire waveguide section. For a 100 mmsapphire waveguide section lower losses were obtained than for a 100 mm standard metal waveguide section.6. Characteristics of a dielectric rod antenna were measured.