Abstract: The boundary condition, which must be satisfied while computing the resonant frequencies of cylindrical dielectric resonators used in microwave circuits with the finite-difference method, are dealt with by introducing fiotioious variables. This paper describes in detail how the boundary conditions are treated. Compared with Pospieszalski's data, the errors in our case are less than 6.8% and 1.7%, respectively. When meshes are properly chosen, errors can be further reduced.