We have presented a self-contained account of the theoretical framework necessary to infer the elastic properties of layered spheres from their forced or free resonance spectra. In support of these results, we have provided numerical and experimental results, limited for external reasons to singly layered bodies. We have also provided graphical aids which enable a rapid and fairly accurate determination of compressional and shear velocities for a homogeneous sphere from a single, particular pair of modes. This technique is useful down to Q’s at least as low as 100, although unambiguous interpretation of observed spectra requires recourse to the theoretical spectral amplitudes and application of the interference rules. Theoretical spectral calculations suggest that simple peak-width measurements will not provide the information necessary to infer both compressional and shear attenuations, at least for low-Q materials.