The inverse method is traditionally used to solve elasticproblems. In the present paper this method is applied for a piezoelectriccantilever actuator subjected to a linear distributed loading on the uppersurface. Nonlinear body force $F_z $ is also considered. The stress functionand induction function in the form of polynomials are obtained. The generalsolutions as well as the influence of the distribution profile of body forceon this solution are discovered. From this conclusion the solutions of thecantilever actuator with constant body force and without body force can beeasily found. This work provides a feasible method to study other kinds offunctionally gradient piezoelectric microstructures.