A numerical solution is presented for the problem of stability of elastic cylindrical shells with rectangular cutouts. Reinforcements around the cutouts and other discrete stiffening elements are considered and the loading can be either axial or lateral. The analysis is based on a two-dimensional finite difference scheme, and thus the numerical solution entails treatment of a large system of nonlinear algebraic equations. A straightforward Newton-Raphson method requires an excessive computational effort, therefore, a modified Newton method is employed in which the iteration strategy is controlled internally during the computation. Simple experiments were performed for the verification of the analysis. The agreement between test and theory appears to be satisfactory. The effects of cutout dimensions and of reinforcement around the cutouts are demonstrated by numerical examples.