A three-dimensional analysis of Whispering-Gallery modes (W. G. modes) in a coaxial dielectric resonator is proposed and presented. The coaxial dielectric resonator is constructed from a lossy dielectric disk and ring which have diameters of several tens times as large as wavelength. Eigenvalue equations of the W. G. modes are derived rigorously from field expressions and boundary conditions. The resonant frequencies, unloaded Q values and field distributions are calculated numerically from the eigenvalue equations. These calculated results are in good agreement with experimental ones for an X band model. As a result, it is shown that a considerable quantity of modal energy can be confined in a loss-less gap between the disk and ring, and then the unloaded Q value is higher than that of a conventional dielectric disk and ring resonator.