By using high dielectric constant and low‐loss dielectric material such as quartz, alumina, or sapphire and by specifically configuring the waveguide structure, we have succeeded in designing a waveguide for the millimeter/submillimeter wavelength range which yields an attenuation constant for the dominant mode that is more than 100 times below that for an equivalent circular dielectric rod with identical cross‐sectional area. This waveguide takes the form of a thin dielectric ribbon surrounded by lossless dry air and possesses an attenuation constant as low as 20 dB/km. Analytical results on the attenuation constant and field extent of the dominant mode on this ribbon structure for several promising materials are given. Experiments have also been performed on ribbon guides made with rexolite. Excellent agreement was found between predicted and measured results.