This study is limited to study of buckling analysis of a sandwich cylindrical shell with functionally graded face sheets and homogenous core. High-order sandwich plate theory is improved by considering the in-plane stresses of the core that usually are ignored in the analysis of sandwich structures. Assume that all properties of the face sheets and the core are temperature dependent. Strain components are obtained by using the nonlinear Von-Karman type relations. The equilibrium equations are derived via principle of minimum potential energy. Analytical solution for static analysis of simply supported sandwich conical shells with functionally graded face sheets under axial in-plane compressive loads and in the temperature environments is performed by using Navier’s solution. The results show the critical dimensionless static axial loads are affected by the configurations of the constituent materials, compositional profile variations, temperature and the variation of the sandwich geometry. The comparisons show that the present results are in the good agreement with the numerical results.