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In this paper, a model was developed for cutting through wax using an ultrasonic instrument in the shear mode. The model was based on viscous heating in a liquid layer of molten wax and extrusion of the molten wax away from an advancing blade, using an energy-balance approach. The model provides a set of equations representing cut rate as a function of velocity and normal force. Using two parameters in the model determined by a regression of experimental data at a single frequency, the model accurately reflected the behavior of experimental data at other frequencies and using blades of different geometries.