Low-frequencies and free vibration modes of the construction consisted of a closed circular cylindrical shell joined with the end cap (plate or cupola) 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 cap frequencies. The frequencies of the second type vibrations slightly differ from frequencies of the cylindrical shell. In the approximate analysis the third type vibrations of the structure is considered as beam vibrations with circular cross-sectional area. Two different asymptotic approaches are used to get approximate asymptotic formulas for “cap”-like and “shell”-like vibration frequencies. An optimization problem is formulated, namely, at what minimum values of the curvatures of the shell and cap the value of the minimum natural frequency of the structure is maximum. When solving the formulated optimal problem, the influence of the thickness of the structure is analyzed.