A new concept in sandwich structures, considered in the paper, employs composite facings with internal ribs. The advantage of this approach is related to enhanced local stiffness and strength of the facings. In particular, the material of facings can be redistributed making the facings thinner, while using the released material for internal ribs. Obviously, this means that the weight of the structure remains without change, while local strength and stiffness increase. The penalty for using this approach is a potential decrease of global stability and global strength as well as lower natural frequencies. The present paper addresses the stability problem for cylindrical shells and panels subjected to axial compression. Buckling loads are calculated for short, complete, cylindrical shells. Based on the numerical results discussed below, it is obvious that ribs should be symmetrically located with respect to the middle surface of the shell. Then a decrease of global stability is relatively small and the proposed design is justified and feasible in practical applications.