At first, an analytical procedure to determine the linear buckling loads of the cylindrical sandwich shells subjected to the external pressures is derived based on the variational method. The method is compared with other analytical method, and the effects of the mode in circumferential direction to the linear buckling loads and the components of the energy of the members are examined. Furthermore, the elastic buckling strength of the members in considering the scatter of the initial imperfection is proposed based on the reduced stiffness method, and these strength are compared with those obtained by the finite element method.