<p>The present paper is an examination of the axisymetric oscillation problem in infinite and finite cylindrical shells supported by two circular frames and hinged at edges.The solution of the problem determining trapped frequencies and modes of an infinite length shell has been found. The conditions under which trapped modes of an infinite length shells become natural frequencies of the finite length shells are determined. It is shown that trapped modes become multiple natural frequencies of the second order of the finite length shell. The cylindrical shell localized modes corresponding to these frequencies are also presented. The peculiarity of such oscillations is their localization along the length of the shell. The investigations shows that the existence of the real discrete frequency above the cut-off frequency must be considered in the design of the engineering structures.</p>