A solution is presented for the dynamic response of a solid sphere of linear viscoelastic material bonded to a mating, rigid spherical cavity which undergoes harmonic excitation. The dynamic response in the form of complex mechanical impedance is obtained in exact analytic form for two types of excitation of the rigid spherical boundary; rotation about a diameter and translation along a diameter. For the purpose of showing the usefulness of this system for experimentally determining the general stress-strain characteristics of the linear viscoelastic material, the sensitivity of the complex mechanical impedance of the sphere in each mode of excitation is examined relative to variations in the complex dynamic shear modulus and complex dynamic Poisson’s ratio of the material.