The vibration and damping characteristics of three-layered cylindrical shells with a viscoelastic core constrained by isotropic facings are studied by using the finite element method. The finite element developed for the study has separate rotations in its displacement field for the core and facings. The element has three nodes and seven degrees of freedom per node. Results are presented for cylindrical shells with different core to facing thickness and length to radius ratios and three boundary conditions: clamped-clamped, simply supported and clamped-free. The effects of the shear parameter on the frequency and loss factors for various geometric properties and boundary conditions are also discussed. © 1994 Academic Press Limited.