Resonant frequencies and unloaded Q's of hybrid modes on cylindrical dielectric resonators in conducting enclosures are studied. The formulation uses the mode matching technique, and includes axially symmetric (TE0mand/or TM0m), as well as axially non-symmetric hybrid (HEnm,) modes which could exist in dielectric loaded waveguides. The structures analyzed can simulate resonators on ground plane backed or suspended substrates. Losses in the conducting walls, substrates, and the dielectric material, and stored energy in the general resonator are obtained. Mode amplitudes determined from the solution of the boundary value problem by mode matching are used to rigorously compute the unloaded Q's of the resonators. Numerical results in the millimeter wave range and in C-band are presented. These results include unloaded Q's and mode charts of dielectric resonators on ground plane backed and suspended substrate structures. From these results, methods for improving the unloaded Q's and mode's separation are explored. Experimental results are presented which verify the accuracy of the model used and the numerical computations.