This investigation presents new practical achievements concerning the velocity of dielectric recovery process inside a vacuum interrupter chamber. According to Andrews-Varey equations, a new model is developed using Matlab-Simulink software. This model is used for doing a new research on inter electrode plasma diffusion, which is the most important factor during insulation recovery interval. The developed model is performed so that it can predict the ionic sheath expansion velocity and post-arc current waveform caused by transient recovery voltage (TRV). One of the faced challenges is to obtain plasma parameters to be utilized based on the previous experimental results. Considering the initial conditions and the related software model Applied to nine different contact materials, and similar 100A quenching current, the achieved results are investigated in details. The main goal is to specify the influence of material (ion mass) and other parameters on the speed of inter-electrode plasma dispersion and voltage recovery process which will guide the designer towards selecting suitable contact material with regard to TRV waveform. Furthermore the effect of TRV value which is applied to the chamber is also investigated in details. In future works this model may be developed so that it can be applied to new metallic alloys made of doped various chemical elements.