Many successful developments and microscopic studies have been made on the high quality insulating materials. However, a little attention have given to the macroscopic interface in HV(High Voltage) insulating systems. In this study, AC interfacial breakdown strength and V-t characteristic of the interface between Epoxy/EPDM(ethylene propylene diene terpolymer) are investigated. Electrode system is designed to reduce the charges from electrodes and to have the tangential potentials along the interface between Epoxy/EPDM by FEM(finite elements method). The AC breakdown strength is observed when HV is given to the interface. It is shown that AC interfacial breakdown strength is improved by increasing interfacial pressure and oiling. In particular, it was saturated at certain interfacial pressure level. V-t characteristic is able to extend to the life time of the interface between Epoxy/EPDM. Oiling also plays a good roll in prolongation of the life time.