The insertion of lithium into electric anode in a lithium-ion battery results in local volume expansion and creates compressive stress in materials. To relax the compressive stress, structural damage including microcracking and local buckling can occur. Using the theory of diffusion-induced stress and the energy principle, analytical relations between the critical concentration of solute atoms and average damage size are established for the insertion-induced cracking and buckling in an elastic film. Numerical results show that surface cracking will prevail over local buckling in accord with experimental observation. For local buckling of a given size, there exists a minimum critical concentration which is determined by the film thickness and the ratio of the Dupré constant to Young's modulus of the film.