A cosmetic implant comprises a filament made from a biocompatible elastomer. The elastomeric filament can be injected or pulled under one or more wrinkles. Once implanted under the wrinkle(s), the filament lifts and supports the tissue above it. Such lifting lessens (and possibly removes altogether) the appearance of the wrinkle(s). The biocompatible elastomeric filament is preferably made from a polyolefinic copolymer material having a triblock polymer backbone comprising polystyrene-polyisobutylene-polystyrene, which is herein referred to as "SIBS"; or alternatively can be made from silicon rubber, expanded polytetrafluorethelyene (ePTFE), polyurethane, polyolefin, copolymers of nylon, copolymers of polyester, or elastin.