Propagation constants for TMon and TEon modes in a circular waveguide with a ring type dielectri are computed using the numerical analysis when the width of dielectric is varied regularly. This structure can be applied to the supporter to make improve the Q-factor of dielectric resonators, and the results of numerical calculation can be used to design the slow wave structures. Also, the numerical analysis in this paper can be used to determine the resonant frequencies in dielectric resonators.