This paper reports a study into the stability of a shell structure of the barrel-ogive type, supported by the discretely arranged intermediate frames, under the joint action of the uniform external pressure and axial compressive efforts. A case of the sinusoidal approximation of the meridian of the middle surface of shell compartments has been considered. Governing differential equations have been built to study the stability of a compound shell structure taking into consideration the curvature radii of the "barrel" and "ogive" compartments under the joint action of axial compression and uniform external pressure. A finite difference method has been used to integrate the fourth-order governing equations with variable coefficients. It is shown that an increase in the meridian curvature parameter exceeding 4 % leads, in some cases that involve the loading by axial forces, to an increase in the critical external pressure by 1.5‒2 times. The effect of stabilizing the growth of critical pressure with an increase in the rigidity of the frames is illustrated for the different values of the meridian curvature and the number of supporting elements. A given effect makes it possible to draw conclusions about the possibility of determining the rational rigidity characteristics of the structure. The effect of increasing critical pressure in the presence of a compressive force in the shells of the positive Gauss curvature, which is the result of internal stretching efforts in the circumference direction, has been investigated. In this case, a generatrix deviation from the ideal shape leads to an increase in wavenumbers in the circumferential direction while the stability is lost, which indicates an increase in the critical pressure. A further increase in the axial compression of the structure leads to the emergence of annular compressive efforts, which is a consequence of the reduction in the critical stresses of external pressure