1. The calculations for cylindrical shells presented for various conditions of fixing show that the magnitude of the initial failure load and the type of initial failure depend both on the structure of reinforcement of the plating and the character of strengthening, and on the mechanical characteristics of the materials of the reinforcement and the bonding agent. 2. The initial failure load will be the greatest, if the entire material of the rib layer is placed into ribs of the circumferential direction. At the same time the specific volume content of filaments of longitudinal reinforcement of the plating must correspond to the abscissa of the pointa1 and A*1 (marked with circles in the figure). 3. For the shell with ends a qualitative agreement with the experimental data from [9] has been obtained.