In this paper, using a differential equation introduced by one of the authors, the behaviors of a cylindrical shell with periodic circular cut-outs under uniform external bending are analyzed, and the deformation, stress distributions and the flexural rigidity of the shell regarded as a beam are discussed. The method of analysis proposed in this paper has no restrictions with respect to the shape, size and the number of cut-outs. As the cut outs get closer to each other, the distribution of the radial displacements near the cut-out shows a complicated character under the influence of the cut-out. On the other hand, the value of stress concentration factor at a middle cross section and the flexural rigidity of the perforated shell are reduced.