Ultrasonic converters, horns, and nondestructive inspection transducers can be accurately designed using the one dimensional (1D) wave equation. The segments that form the resonant power driver and the backing and matching layers and the piezoelectric element of an inspection transducer are modeled by applying the wave equation for each segment. Equilibrium of stresses and continuity of displacements at the interfaces are used to join the segments together. But as the need to scale up ultrasonic processes for a variety of applications continues to grow, larger drivers that are more complicated in shape must be designed. Models based on the 1D wave equation are no longer suffi cient.