The wire electrical discharge machining process is one of the earliest special methods of production or nontraditional machining methods. High precision and possibility of high strength material machining are some advantages of this method, so that in some cases it is the only method of machining. The relatively long machining time and consequently the high machining cost and also necessity of work piece conductivity are the disadvantages of this method. In order to prevent wire abrasion and tearing in the wire cutting process a constant velocity is used for the wire whereas the work piece remains fixed. However, concerning the short time of the electrical discharge and the small relative velocity of the work piece and wire, this velocity has a little effect on the molten hole. In new machining methods such as wire electrical discharge turning and grinding, a rotational velocity is considered for the work piece. Thus, the relative velocity of the work piece and wire considerably increases and it causes the expansion of the molten hole and change of material removal rate and surface roughness. In this research, the electrical discharge process simulation is modeled by FORTRAN coding in the finite element software ABAQUSE and its effect on the material removal rate (MRR) and the elongation rate of the molten hole are studied. The temperature dependency of material properties and expansion of plasma channel radius with time have been employed in the simulation. In the second stage vibratory motion of the wire is simulated and its effect on the material removal rate is investigated. By wire vibratory motion normal to relative motion direction, the material removal rate increased. It was found that a better correlation with experimental results is achieved when the latent heats of fusion and evaporation are taken into consideration, as well as temperature-dependent thermo-physical properties of the work piece. The developed model of this research is validated by reported experimental result K e ywords: Wire EDM; Thermal modeling; FEM; material removal rate (MRR); elongation rate;