Stretchability enables the device to be patched to a curved surface or to be folded several times to maximize usability. Among many methods, the pre-strain method is advantageous in that the stretchability as much as the pre-strain applied to the substrate is guaranteed even without material improvement. When the pre-strain is restored to its original state, the thin film gets wrinkled or the substrate gets buckled. Wrinkles and buckling that appear in this way are affected by the physical properties and dimensions of the substrate, and it is necessary to analyze their effect. In this study, a theoretical approach was used and a nonlinear post-buckling analysis was performed using a finite element method. The analysis was divided into two steps: the pre-strain step and the recovery step. According to the analysis results, it was possible to predict and analyze the wrinkle and buckling behavior due to pre-strain according to the physical properties and dimensions of the substrate. The pre-strain analysis method can be applied to multi-layer structures with three or more layers and can be used as a method to analyze wrinkle suppression and wrinkle shape control in future studies.