A computational model is constructed and an algorithm for investigation of the stability of a three-layered sloping shell supported by transverse stiffness ribs is developed. The variational method, based on the principle of possible displacements, is used to derive the differential stability equations for the region of the shell enclosed between the edges, as well as the conditions along the edge lines and along the edges of the shell. There was developed a program for the numerical implementation of the author's methodology, it was implemented in the Wolfram Mathematica environment. It is shown that there is a finite value of the moment of inertia of the ribs that supports the shell, at which the maximum critical stress (the critical moment of inertia of the rib) can be reached, which is determined from the stability equation. As an example, we consider a square in plan shell, supported by one and three stiffness ribs. The values of the critical moment of inertia of the rib are presented, which were determined both with regard to the edge Reissner effect and without taking it into account. The dependences of the critical load parameter on the linear dimensions of the shell, reinforced by one and three transverse stiffness ribs, are plotted.