A simple model is reported for thickness-mode piezoelectric elements used as ultrasonic transducers in measurement systems. The model represents the excitation system and transducer as a Thevenin mechanical equivalent for the transmitting mode and a Thevenin electrical equivalent for the receiving mode. Computer programs based on the model have been developed, and computer simulations to study the effects of backing materials, element areas, and excitation sources are reported. The nature in which the source impedance alters the Thevenin mechanical output impedance and its importance in determining peak transmission frequency and in computing acoustic coating layers for matching was found. A total transfer improvement of 28 dB was shown for epoxy-backed elements radiating into fluid with the transducer used as both transmitter and receiver by using high values of source and load impedances in contrast to low values. The model was found to agree closely with experimental data of a 2.7-MHz transducer. Subject Classification: 85.40; 80.70; 85.52.