Atheory is outlined of sandwich box-typecomposite shells designed to withstand a combination ofthermalloading,internalpressure,torsionalandaxialloads.Acrosssectionoftheshellrepresentsa rectangularboxwithcurved cylindrical sections at the corners. The facings of the shell are dissimilar to maximize their efe ciency, according to the loads acting on each facing. This approach enables a designer to optimize the structure by maximizing the load-carrying capacity or minimizing the weight. The formulation includes the following developments: 1 ) global theory of a sandwich shell composed ofrectangular and cylindrical sections, where equationsof motion are formulated based on a e rst-order shear deformable version of Sanders’ s shell theory; 2 ) theory for local deformations and stresses in the facings, where the facing is treated as a thin geometrically nonlinear plate or shell on an elastic foundation using von K´