In this paper the analytical method has been used for solving the problem of vibrations of the three-layer shell with damping. External layers are modelled as the MINDLIN shells and the internal layer possesses the characteristics of a viscoelastic one-directional WINKLER foundation. Small transverse vibrations of the three-layer shell with damping is excited by the dynamical non-uniform loading moving at the constant velocity $v*$. Numerical results are presented in the diagrams.