Ultrasonic assisted creep feed grinding of hard-to–cut materials such as superalloys is a novel technique for ease of the process and elimination of use of cutting fluids. In this research the effects of longitudinal ultrasonic vibration of workpiece in dry creep feed grinding process is investigated. The mechanism of abrasive grain and workpiece interaction in the presence of ultrasonic vibration has been analysed both analytically and numerically. Then, the results have been compared with experimental findings. This research covers only geometrical modeling of the process and other aspects are out of scope of this work. The cutting path of a single grain in ultrasonic assisted grinding has been derived using equations of motion and has been compared with the grain-cutting path in ordinary grinding. The calculations have shown that there is a multiple and discontinuos cutting along the contact zone. By Impelementing a 2-D finite element modeling in commercial Msc. superform software, the mechanism of chip formation in ultrasonic assisted grinding and ordinary grinding has been compared. In the present work the effects of longitudinal workpiece vibration on the grinding forces and grinding power of Inconel738LC has been investigated. The obtained results show that the application of ultrasonic vibration can decrease the grinding forces. A decrease of up to 27% of vertical grinding forces and up to 22% of horizontal grinding forces has been achieved. FE analysis of abrasive grain and workpiece interaction under ultrasonic vibration has shown a reduction of about 40% of grinding forces compared with ordinary grinding. Depth of cut was Chosen to be 25 and 50 Microns, but thermal expansion of the workpiece (due to grinding thermal effects), was creating an actual depth of cut which was much higher than the setting values. Maximum overcut in ultrasonic assisted grinding was 116 micron whilst it was 128 micron in ordinary grinding. Moreover, maximum grinding power has shown a reduction in ultrasonic assisted grinding compared with ordinary grinding power. Reduction of grinding forces and power not only results in improved surface integrity but also it increases the possibility of grinding without cutting fluids. Key words Ultrasonic assisted grinding, Numerical modeling, Creep feed grinding, Ultrasonic, Superalloy