The three-layer shells, their stability from external loads, are devoted to a huge literature, but nevertheless, even for the case of a circular cylindrical shell, there are no systematic studies. The purpose of this book is, not only to obtain as simple formulas as possible for calculating critical loads, but also to find out the effect of geometric parameters of the shell and elastic parameters of their material on the critical load value for the entire practically occurring range of changes in these parameters. The solutions of problems for the cylindrical shell and panel, for the comic shell under various external loads and boundary conditions. These solutions are based on linearized sheath stability equations, which are considered thin and elastic. Nevertheless, the general theory is developed for the final deflection of shells having an asymmetrical thickness structure, rigid outer layers and fillers that transmit both forces in their own median surface and moments; the filler also transmits a transverse shift. The distribution of transverse shifts is given in the general form. It takes into account the deviation of the surface from the ideal shape.