Abstract: In this paper, based on Ref. [1] the axisymmetrical buckling of simply supported cylindrical sandwich shells under the action of uniform axial lood is solved by a rigorous method. The classical theory of shells is used for the two face sheets and the core is considered as a three-dimensional elastic body. A series of transcendental equations are obtained, from which the critical loads can be calculated by manericai methods. Numerical examples are given to compare with the solutions of sandwich shell theories.