Abstract: Controlling the surface instability of the film/substrate structure has been utilized to fabricate stretchable electronic devices. However, because these devices undergo external loading, the residual stress is concentrated at the interface between the film and substrate, and the problem of interfacial debonding and delamination for film/substrate structure is induced. By means of theoretical analysis and numerical simulation, the buckling behaviour of the piezoelectric thin film/substrate structure is investigated. Due to the characteristics of larger displacement but small strain for the deformed film, the film is modelled as a nonlinear Bernoulli-Euler beam and the theoretical analytical model for this film/substrate structure with no buckling, wrinkling, partial delamination and total delamination is established via energy minimization principle. The critical strain expressions for the evolution between no buckling, wrinkling, partial delamination and total delamination are obtained; Numerical examples are carried out to verify the correctness of the proposed formulations and, to analyze the influences of geometrical and material parameters of this structure on wrinkling behaviour. From the results of this study, one can conclude that the wrinkling pattern of this structure can be controlled by changing the Young's modulus, pre-strain, physical fields, and interface adhesion coefficient. By modulating the temperature change and voltage, this structural wrinkling pattern can also be fine regulated. And the findings of this study are useful and helpful for the design of piezoelectric film/substrate-type stretchable electronics.