The extension of the equations of Stein and Mayers to include application to inelastic buckling of orthotopic sandwich shells for those classes of loading for which torsion does not act in combination with axial or lateral forces is presented. A deformation theory of plasticity is used to evaluate the 12 remaining orthotropic rigidities for rib-cored sandwiches. The solution for the critical buckling pressure is given for loading by external hydrostatic pressure. The effect of Poisson’s ratio is discussed, and corrections for the elastic compressibility are presented. These corrections permit a smooth transition from elastic to inelastic solutions.