Advanced technologies and complex systems in different industrial areas such as electronics, aerospace, medicine, optics, and so on require producing parts with high surface quality and low roughness. To this end, different non-conventional methodologies such as electro discharge machining, electro chemical machining, laser beam machining, and so forth are proposed for machining and polishing parts that each one has pros and cons. Applying advanced abrasive ceramic grits for polishing is one of the prevalent techniques that has attracted researcher and manufacturer’ s attention to produce high precision workpieces. Beside minimum thermal and chemical side effects of abrasive powders on the workpieces, this technique can be applied with various types of energy such as hydraulics, pneumatics, magnetics, and etc. Abrasive polishing uses vibration energy to generate kinetic energy in the powders in order to polish the surface of the parts. even though this method was applied for many years, , , There are some unkown aspects of this process. The focus of this work is on the mathematical modeling and numerical simulations which is done recently by some of researchers in this field.