This paper pays attention to predicting the nonlinear bending behaviors of functionally graded materials (FGM) infinite cylindrical shallow shells with a two-parameter elastic foundation by using a two-step perturbation method. The shells are subjected to uniform temperature rise and temperature dependency of the constituents is also taken into account. Two ends of the shells are assumed to be clamped or pinned and in-plane boundary conditions are immovable. The governing equations are derived based on physical neutral surface concept and high order shear deformation theory. The explicit expressions between the transverse load and the deflection are obtained by perturbation method. In numerical examples, some comparisons are shown to verify the correctness of the present research and solution method. It can be concluded that FGM cylindrical shallow shells subjected to uniform bending loadings will bring about snap-through buckling and jump changes, and the foundation can enhance the stability of the shells. (C) 2017 Elsevier Ltd. All rights reserved.