Low frequencies and vibration modes of a closed circular cylindrical shell joined with annular plates are obtained by means of asymptotic methods. Two types of vibrations, corresponding to narrow and wide plates, are analyzed. It is shown that narrow plates can be considered as circular beams. For wide plates joined with a cylindrical shell the couple vibration problem in the first approximation is reduced to the eigenvalue problem describing the plate vibrations. An approximate solution of the last problem is obtained with the help of the perturbation approach.