In recent years, the ultrasonic elliptical vibration cutting (UEVC) technique has been found to be an efficient method for the ultraprecision machining of hard and brittle materials. During the machining at a given nominal depth of cut (DOC), the UEVC technique, because of its inherent mechanism, effectively reduces the thickness of cut (TOC) of the workpiece material through overlapping vibration cycles. For the ductile machining of hard and brittle materials, this TOC plays a critical role. However, the relationships between the nominal DOC, the TOC, and the relevant machining parameters have not yet been studied. In this study, the role playing machining parameters for the TOC are firstly investigated and then theoretical relations are developed for predicting the maximum TOC with respect to the relevant machining parameters. It is found that four machining parameters, namely, workpiece cutting speed, tool vibration frequency, and tangential and thrust directional vibration amplitudes, influence the . If the speed ratio (ratio of the workpiece cutting speed to the maximum tool vibration speed in the tangential direction) is within a critical value 0.12837, then a reduced can be obtained. It is also realized that if the can be kept lower than the critical DOC , then ductile finishing of brittle materials can be achieved. The above phenomenon has been substantiated by experimental findings while machining a hard and brittle material, sintered tungsten carbide. The findings suggest that the same concept can be applied for the ductile cutting of other hard and brittle materials.