This paper presents the solution for the nonlinear postbuckling behavior of a cylindrical sandwich shell with face sheets of a homogeneous material and a core of an isotropic shear-resistant material. Effects of inelastic behavior are neglected. The principle of minimum potential energy is used in the derivation of the compatibilit}^ equation. Also determined from this principle are three equations of equilibrium to be solved simultaneously with the compatibility equation. The four unknown functions appearing in the equations are a stress function, a normal displacement component, and two shear-deformation components. A Ritz method of solution is used to reduce the four partial differential equations to a set of five nonlinear algebraic equations whose unknowns are parameters in an assumed form of the solution for the normal displacement component. Limiting solutions of these equations are compared with the works of Kempner, Teichmann, Wang, and Gerard. These algebraic equations are solved by a numerical scheme on an IBM 704 computer, and the results, which represent approximate postbuckling behavior, are plotted. These results are then compared with those of March and Kuenzi.