In the modelling of thin-sheet piezoelectric actuators the effect of bending of the actuator itself is usually ignored. The current paper presents a model of a surface bonded piezoelectric actuator subjected to electric loading, which contains both the axial and bending deformations. The static electromechanical response of the actuator is studied under different mechanical and geometrical conditions to evaluate the effect of bending. An imperfectly bonded interface is proposed to simulate debonding and to study its effect on the actuation process. The problem is formulated as integral equations in terms of the interfacial shear and normal stresses, which are solved by using Chebyshev polynomials. Based on the solution, the effect of bending of the actuator upon load transfer is analysed. Illustrative examples are presented to show the effect of the material property, the geometry and the interfacial debonding on the response of the integrated structure.