Dynamic stability of a sandwich cylindrical shell, supported by both the annular ribs and the cylinder, loaded with external pressure, changed harmonically, is investigated. The normal and tangential components of contact interaction between the shell and ribs are accounted. The cylinder is presented as elastic foundation with coefficient of soil reaction that defined from equations tridimensional theory of elasticity. Solution of differential equations is found in the shape of trigonometric sequence. As a result, the problem reduces to the system of algebraic equation in reference to components of shell’s displacement in the ribs installation places. The number of equation is three for ribs are installed regularly. In the numerical example shows the effect of the ribs and cylinder to the shell’s instability domain.