The applications of dielectric resonators are currently of considerable interest in microwave integrated circuits. The design of a dielectric resonator depends on its natural resonant frequencies. Since exact solutions of dielectric rectangular and cylindrical resonators cannot be rigorously computed a new and more accurate method has been developed to solve this problem. In this method all the surfaces are simultaneously considered as imperfect magnetic walls. Theoretical values agree very well with experimental results. The difference being less than 1 percent.