Nonlinear stress-strain relationships (physical nonlinearity) may have a large effect on the structural response of piezoelectric sensors and actuators. The paper addresses the subject concentrating on cylindrical piezoelectric rods that experience vibrations as a result of an alternating electric field applied in the axial direction. The problem considered in the paper is important in connection with design of piezoelectric transducers. It is shown that neglecting the non-linear stress-strain relationship of the piezoelectric material can result in a significant error in the predicted response of the transducer.