In this paper, the estimation of lifetime with the various conditions of the interface between toughened epoxy and rubber which are consisting materials of underground power delivery system has been studied. After the measurement of the short time AC interfacial breakdown strength on macro interfaces at room temperature, the breakdown time at several voltages were measured under the constant voltages lower than the short time breakdown voltage. The long time breakdown voltage was calculated by using Inverse Power Law. Two types of interfaces was studied. One was the interface between toughened epoxy and EPDM(Ethylene Prorylene Diene Terpolymer). The other was the interface between toughened epoxy and silicon rubber. Interfacial pressure and roughness of interfaces was determined through the characteristic of short time AC interfacial breakdown strength. Oil condition was no oiled, low viscosity oiled and high viscosity oiled. High viscosity oiled interface between Toughened epoxy and silicon rubber had the best lifetime exponent, 20.69. and the breakdown voltage of this interface after 30 years was evaluated 19.27㎸.