The paper deals with the stability of an elastic non-circular cylindrical shell of intermediate length under uniform external pressure. The shell is assumed heterogeneous in the thickness direction, in its part it may be multilayered. In order to derive the equations of stability, we use the generalized Timoshenko-Reissner model. According to it, a shell that is heterogeneous can be replaced by a homogeneous shell with the equivalent bending and transversal shear stiffness.We obtain the approximate asymptotic formula for a critical load that takes into account an influence of a transversal shear and a variability of a directrix curvature. This formula generalizes the classical Southwell-Papkovich formula for a circular homogeneous shell.As an example, a three-layer elliptical shell is analysed, with hinged edges and a soft middle layer. We discuss the influence of transversal shear on a critical load for both an elliptical and a circular shell.