The buckling under the uniform external pressure of a thin elastic circular cylindrical shell stiffened by the rings of the T-shaped cross-sections is analyzed. The narrow rings are considered as circular beams. The wide rings are treated as annular plates stiffened at one edge by a circular beam. In the both cases problem is reduced to solution of the eigenvalue problem for systems of linear differential equations containing a small parameter. By means of asymptotic approaches approximate formulas for the critical pressure are obtained. The optimal parameters corresponding to the maximal critical pressure of the ring-stiffened shell with a given mass are evaluated.