Summary For a number of applications like structural wave mechanical testing and low coupling resonant sensors, the understanding of the interaction of piezoelectric transducers with the structure at low frequencies is important. Here, one-dimensional models are developed for the excitation of longitudinal and bending waves in rods by transducers with and without backing material. The transfer functions computed from these models are compared with experiments. It is found that at low frequencies, where the properties of the piezoelectric transducers are of minor importance, good agreement can be found between theory and experiment. For higher frequencies, unwanted resonances, in particular, have a strong influence on the transfer function observed. For the excitation of bending waves, a notch is predicted and observed experimentally at a wavenumber, which is approximately determined by the ratio of mass per unit length of the rod and the transducer rotatory inertia as primary parameter, if this ratio is sufficiently large.