Results are presented of a study of the free vibration and damping characteristics of spherical shells with constrained viscoelastic core. A finite elements based on discrete layer theory was used for the analysis. Calculations were carried out for different parameters, such as the shear modulus of core, the opening angle (shallowness), the total thickness to radius ratio, the core thickness ratio, the core location and the boundary conditions. © 1994 Academic Press Limited.