<p>We propose a general procedure for estimating eigenvalues within the framework of a problem posed for an elastic thin-walled closed shell. According to this procedure, the problem is reduced to an eighth-order differential equation. Its idea is based on the decoupling of the problem into two simpler problems, namely, a two-dimensional elasticity problem and a thin-plate problem. Both problems are reduced to a biquadratic equation. If we choose one of these problems as the main problem, then the eigenfunctions of the second problem can be represented in the form of a linear combination of functions obtained from the main problem. The obtained eigenvalues are compared for the four most popular cylindrical-shell theories for the case of concentrated radial loads. The results slightly differ only for small numbers of the terms of circumferential mode expansions and are in good agreement with the results obtained earlier by using different semianalytic methods.</p>