The paper considers natural oscillations of the three-layered cylindrical shells filled
by an elastic medium. The Kirchhoff-Love’s hypotheses are accepted for the thin isotropic bearing layers. The work of the transverse shear and thickness reduction in the thick filler are taken into account. Variations in displacements in the transverse coordinate are accepted to be linear The conditions of continuous displacements are used on the contact boundary.
The reaction of the inertia-free elastic filler is described in terms of the Winkler’s model.
A number of analytical solutions have been obtained and numerical analysis according to the frequencies of the natural oscillations.