An antenna made of a dielectric disk with a high permittivity mounted on top of a grounded dielectric substrate of low permittivity is analyzed. A numerical procedure based on surface integral equations, derived from the equivalence principle, is used to compute the natural resonant frequencies for the HEM11 mode from which the radiation Q factor of the antenna is obtained. Then the radiation pattern of the antenna, operating at the resonant frequency evaluated previously, is computed with an electric dipole excitation located within the dielectric substrate under the dielectric disk. The effect of various parameters on the radiation characteristics of the antenna is studied, and presented in the form of diagrams. The low values of the radiation Q, combined with the high values of the dielectric Q and conductor Q, indicate that this antenna promises to be more efficient than the microstrip antenna.