Non-linear static deformation, combined with small vibrations in its vicinity, of an imperfect cylindrical panel under axial loading, is studied within a single-degree-of-freedom treatment. The frequency of the small vibrations vanishes at the limit load. This conclusion is proved to be valid for a system with any other non-linearity as well. Special emphasis is placed on the influence of initial imperfections on the vibration frequencies. © 1987 Academic Press Inc. (London) Limited.