Low-frequencies and vibration modes of the construction consisted of a closed circular cylindrical shell joined with the circular plate are obtained by means of numerical and asymptotic methods. Three types of vibrations are analyzed. The frequencies of vibrations of the first type are close to plate frequencies. The frequencies of the second type vibrations slightly differ from the frequencies of the cylindrical shell. Two different asymptotic approaches are used to get approximate asymptotic formulas for plate-like and shell-like vibration frequencies. In the approximate analysis the third type vibrations of the structure may be considered as beam vibrations with circular cross-sectional area. The optimal ratio of the plate and shell thicknesses that provides the maximum value of the fundamental frequency of the structure with the given mass is evaluated. The asymptotic and numerical results obtained with FEA are in good agreement.