Fundamental buckling property of human facial skin is addressed to understand the effects of epidermal aging on the formation of prominent wrinkles. We have proposed a new wrinkle formation theory that the prominent wrinkles suddenly appear with aging by the buckling mode switch from the horny buckling to the epidermal buckling. In this theory, the epidermal aging plays an important role in promoting the enlargement of wrinkles. Focused on the epidermal aging, dependency of the buckling property on Young's modulus and thickness of viable epidermis is evaluated through the linear finite element buckling analyses to search for the minimum buckling mode of the infinite-length skin. We found that the change in Young's modulus of viable epidermis more predominantly affects the buckling mode switch than the change in epidermal thickness.