This paper discusses the vibration behavior of the wire to arrive at a general equation for the wire deflection. The movement of wire between upper and lower guide creates vibration; vibration is also created during the machining process. The Finite Element Analysis model [FEA] for the wire deflection is analyzed. Since the general equation is unable to be simplified because of its complex nature, certain assumptions are made to simplify the equation and the obtained partial differential equation is solved by the method of separation of variables to generate a displacement function y (z, t). The displacement function will be able to analyze machining of micro parts, which will be used for further research in micro machining which also helps us to choose the parameters such as current, spark gap, wire feed, and the speed of the work piece, has made its contribution for machining of micro parts with the Wire Electric Discharge Grinding [WEDG]. The FEA results and arrived equation result is compared by equating with some sample values for the equation with various chosen wire frequency.