In this paper, boundary integral equations are derived from the Green's identity of the second kind in circular cylindrical coordinates, and are applied to determine the resonant frequencies of shielded circular ring and disk resonators. The integral equations are numerically solved by discretizating the integration path representing the air-dielectric interface and the surface of thick strip conductor. Because of the choice of the eigen-functions as weighted functions instead of Green's functions, the overall integral path length is shortened and computational time is reduced. Computational results on thick circular disk and ring resonators are compared with other available numerical results and experimental data.