In this paper, a novel design for an ultrasonic power transmission system designed for use in aircraft structural monitoring systems is described. The prototype system uses ultrasonic Lamb waves to carry energy along plates, such as those used in aircraft structures, and commercially available piezoelectric patch transducers as the transmitter and receiver. This sets it apart from other acoustic power transmission systems reported to date. The optimum configuration transmitted 12.7 mW of power across a distance of 54 cm in a 1.5-mm-thick aluminum plate, while being driven by a 20-Vpp, 35-kHz sinusoidal electric signal. This is in the same order of magnitude as the power required by the wireless sensors nodes of a structural health monitoring system currently being developed by Cardiff University and its partners. Thus, the power transmission system can be considered a viable component of the power source combination considered for the sensor nodes, which will also include vibration and thermal energy harvesting. The paper describes the design and optimization of the transmission and reception circuits with the use of inductive compensation. The use of laser vibrometry to characterize the transducers and to understand the signal propagation between them is also reported.