The layer of skin that wrinkles as a person get older is:
Dermis
The dermis is a thick layer of living tissue below the epidermis which forms the true skin, containing blood capillaries, elastic and collagen fibres, nerve endings, sweat glands, hair follicles and other structures. Repeated extensions and compressions of the skin cause repeated injuries of the fibres in the dermis. During the repairing process, some of the broken elastic fibres and collagen fibres are not regenerated and restored. This leads to the formation of wrinkles.