NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Flexible dielectric waveguides have been demonstrated at 10 GHz and 94 GHz by filling hollow, low dielectric constant polymer tubes with low-loss, high-dielectric constant powders. Flexible guides with losses as low as 0.12 dB/cm were demonstrated at 94 GHz. These guides also exhibited negligible bending loss for radii of curvature greater than 4 cm. The theory of 3-region cylindrical dielectric waveguide was used to design the powder-filled tube guides, and measured wavelengths for the [...] mode are in agreement with theoretical values. Sets of dispersion curves were calculated numerically from the theory for waveguide parameters typical to our guides. A powder-filled rectangular groove in the surface of a plastic substrate has also been demonstrated as a dielectric waveguide at 94 GHz. Guide wavelengths measured for these channel guides for various combinations of guide dimensions, powders, and substrate materials agree with values predicted by the approximate theory of Marcatili for the [...] mode. Measured transmission losses were as low as 0.09 dB/cm. The 94 GHz loss tangents of the powders were calculated by extending Marcatili's theory to relate channel guide attenuation to material losses. These calculated values of loss tangent increased with powder packing fraction, as predicted by theories of electromagnetic wave propagation in random heterogeneous media. Estimates of the 94 GHz loss tangents of the solid constituent materials were then obtained from these theories using the powder loss tangents. Powder channel ring resonators had Q's as high as 2400 at 94 GHz in an 8 cm diameter ring. Directional coupling from adjacent straight channel guides was used to form a transmission filter. Marcatili's approximate theory of bending loss for channel guide appears to be inadequate for predicting the curvature losses of these resonators. In a 10 GHz experiment, the coupling between two parallel powder channel waveguides was measured as a function of their separation. The measured coupling was at variance with that predicted by Marcatili's approximate analysis for parallel channel waveguides.