A new approximate method for predicting the resonant frequencies and for solving the field distribution problem of a cylindrical dielectric resonator (DR) is developed. The model proposed in this paper bridges the gap between rigorous and accurate finite-element or Green function-based numerical methods on the one hand and on the other hand, simple approximate solutions in which the field distribution can be described analytically, but the resulting frequency is accurate within a few percent only. In the method described here, the approximate solution for the microwave field distribution is modified by substituting different values of the radial separation constants inside and outside of the diskshaped DR. The model is generalized for the double-stacked DR structure and enables one to introduce corrections that take into account the presence of the shielding walls and of the cylindrical sample hole. Good agreement is found between experimental and calculated results for both the single and double-stacked structures that are designed around commercially available X-band DRs (9-10 GHz). For the resonant frequency of the lowest transverse-electric TEzero1 delta mode that is commonly used for EPR measurements, the accuracy of the method is better than 1%. Experimentally measured resonator filling factors are also in good agreement with those theoretically estimated. Both the theory and the experimental results suggest that the double-stacked DR structure with finite spacing between the ceramic cylinders is the most suitable for EPR measurements of long lossy samples.