This study investigates the relation between the material gradient properties and the optimum sensing/actuation design of the functionally graded piezoelectric beams. Three-dimensional (3D) finite element analysis has been employed for the prediction of an optimum composition profile in these types of sensors and actuators. To this end, various static tests for functionally graded piezoelectric beams with different geometric parameters, material gradient index, mechanical and electrical boundary conditions are considered. The obtained numerical results of the present study not only would help the selection of a most suitable volume fraction distribution for the functionally graded piezoelectric sensors and actuators but also give a comprehensive insight about the static electro-mechanical behavior of these structures. Moreover, the present results could serve as a benchmark to assess different one-dimensional functionally graded piezoelectric beam theories.