The reliability of high voltage power apparatus depends upon the careful design of its insulation and configuration of electrostatic field. The most common failure of the insulation occurs due to the surface insulation failure and the discharges within the void. In this regard, the monitoring and prevention of insulation failure becomes essential for uninterrupted functioning of high voltage power apparatus. Hence the deterioration of Insulation in an Insulator is determined from the analysis of Partial Discharge signals. The Partial Discharge signals are produced by the localized ionization within the electrical field. The Numerical Analysis of Electric field can provide information about the Partial Discharges which is determined by using the Finite Element Method. In this paper the electric field analysis are performed using FEM for the Epoxy insulator at various voltages and frequencies. It can provide information about the degradation of insulation well in advance thus avoiding major break down of power system.