A recently developed p-version finite-element program [Bagus et al., IBM Res. Div., Res. Rep., RJ 7733 (71598), October 1990; Carnevali et al., in preparation] was used to simulate the dynamic behavior of an ultrasonic bonding tool. The accuracy of the p-code was exploited to resolve high-order modes near to the ultrasonic operating frequency (approximately 60 kHz). In particular, an undesired high-order bending mode was found to occur at a frequency very close to the axial mode that facilitates the bonding process. An optimal operating frequency that minimizes the excitation of the deleterious mode could be determined. Frequency response simulations and experiments were performed to validate this assertion. Their nature, and the accuracy required to resolve these high-order modes, would have made this analysis extremely difficult with other finite-element tools. © 1991, Acoustical Society of America. All rights reserved.