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In this paper, an analytical approach for global buckling of ring-stiffened sandwich cylindrical shells is presented with layerwise theory (LWT). Appropriate displacement functions are assumed according to the boundary conditions and the deformation characteristics of the inner and outer shells. The strain energies of the inner and outer shells and the ribs and the work done by external forces are derived with the help of classical laminate theory. Furthermore, the Rayleigh–Ritz method is employed to obtain the critical buckling load of ring-stiffened sandwich cylindrical shells. The ribband width has a great influence on the precision of calculation of the critical buckling load, and a formula for calculating this width is obtained by data fitting. To confirm the accuracy of the proposed formulation, a numerical simulation is carried out by using Abaqus FEM software. The results show that the proposed approach has high accuracy in predicting the global buckling behavior of ring-stiffened sandwich cylindrical shells. Finally, the effects on the buckling performance of ring-stiffened sandwich cylindrical shells caused by changing the inner and outer shell thicknesses and the rib height, thickness, and spacing are explored.