Linearly polarized fundamental mode Gaussian beams were generated and coupled to a hollow circular oversized dielectric waveguide by placing the waist of the beam at the guide entrance. The transmission properties of the waveguide were characterized as a function of frequency for a variety of coupling conditions. These conditions included changes in the input beam waist radius, angle of incidence, and displacement perpendicular and parallel to the guide axis. It has been found that: 1.) power transmission is maximized when the waist of the input beam is centered at the guide input, injected normally, and has a radius of 0.43 times the waveguide radius, 2.) power transmission decreases rapidly with increasing angle of incidence and the rate of that loss increases with frequency, 3.) the waveguide preserves the linear polarization of the input beam, 4.) power transmission in the fundamental waveguide mode is not greatly affected by moderate displacements in the input beam position, and 5.) upon exit from the waveguide the launched EH11 mode propagates as a fundamental mode Gaussian beam in the quasi-far field. The results compare favorably to the transmission theory of Belland and Crenn and approximately to the near and far field mode pattern theory of Degnan.