Dielectric resonators (DR's) are widely used in telecommunication systems. A method is proposed here to find the resonant frequency and field distribution in a substrate-mounted DR structure. The field of a dielectric rod has been decomposed into a combination of guided modes with unknown coefficients and an unknown continuous spectrum of radiation field. The unknowns are then obtained by applying two generalized impedance boundary conditions (GIBC's) representing the substrate and air layers at the top and bottom of the DR. This leads to the calculation of the total (guided+radiation) field as well as the resonant frequency of the structure. >