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The boundary value problem for wave propagation on a cylindrical anisotropic rod has been solved for hybrid modes, i.e., those having angular dependence. Solutions for the rod radius, normalized by the free space wavelength, as a function of the phase velocity, are presented for various values of the transverse and longitudinal dielectric constants. When the rod is terminated by conducting end plates, a high microwave resonator results. The electric and magnetic energies stored in the rod have been calculated, as has the cavity . Experimental resonant frequencies for various modes in an -band cavity using a ruby laser rod are compared with theory.