We study the stability of a three-layer shell with light filler. The shell is supported by the system of circular ribs. The inner surface of the shell is attached to a hollow elastic cylinder. We consider the shell under an axial compression and external pressure. The ribs may be spaced arbitrary and differ from each other. Using the representation of the displacement functions for the shell and the cylinder in terms of trigonometric series, we transform the problem to a problem for the system of homogeneous algebraic equations. As unknown variables, we use three amplitude components of a displacement corresponding to points of location of ribs; consequently, the number of unknowns is equal to the triple number of the ribs. In t he case when the ribs do not differ from each other and are located equidistantly, we reduce the problem to the problem for a system of three algebraic equations.