In the majority of works devoted to the issues of stability of cylindrical shells filled with a resilient and supported by an array of ribs, as the calculation schemes used by traditional models, which allow the use of well-designed solutions methods. However, during the creation of space technology problem encountered in the “nonclassical” setting when, for example, a cylinder shell length less than the length or the cylinder bore has a cone shape. Obtaining exact analytical solution of such problems is very difficult. Therefore, researchers are using mathematical methods or close or reduce the design to a simplified model. In this paper, by the Bubnov-Galerkin investigated the stability of simply supported pivotally-layered orthotropic shell, supported by circular ribs and isotropic elastic cylinder with a channel portion in the form of a cone under the influence of external pressure, changing along the generator at an arbitrary law. Deformation of the cylinder is described by the equations of the plane theory of elasticity. The problem is reduced to an infinite system of homogeneous algebraic equations, which means the truncation is to the characteristic equation. Effect of taper illustrated by a number of numerical examples.