The properties of degenerate whispering spherical modes within a fused silica and sapphire dielectric resonator have been investigated. However, departure from spherical symmetry occurs due to the support structure and anisotropy of the material. Finite element modeling is used to predicted the lifting of the frequency degeneracy, and is confirmed by experiment. Further optimization of the sapphire resonator to realize a Michelson Morley experiment is discussed. (c) 2006 Published by Elsevier B.V.