Dynamic stability of a sandwich cylindrical shell, sutrtrorted by both the annular ribs and the cylinder, loaded with external trressure, changed harmonically, is investigated. The normal and tangential comtronents of contact interaction between the shell and ribs are accounted. The cylinder is trresented as elastic foundation with coefficient of soil reaction that defined from equations tridimensional theory of elasticity. Solution of differential equations is found in the shatre of trigonometric sequence. As a result, the trrobltd reduces to the systtd of algebraic equation in reference to comtronents of shell’s distrlactdent in the ribs installation trlaces. The number of equation is three for ribs are installed regularly. In the numerical examtrle shows the effect of the ribs and cylinder to the shell’s instability domain.