The stability problem of a shallow sandwich shell of conical segment shape, subjected to uniform external pressure and compression along generators is analysed based on the finitedeformation theory. With the help of the Ritz method the system of five non-linear, heterogeneous equations is obtained. They are the basic equations of elastic stability of the shell under consideration. The results of numerical calculations are presented in diagrams, which show the influence of basic mechanical properties and geometric parameters of the shell on the value of the upper and lower critical load.