A substrate holding apparatus is for holding a substrate such as a semiconductor wafer in a polishing apparatus for polishing the substrate to a flat finish. The substrate holding apparatus comprises a vertically movable member, and an elastic member for defining a chamber. The elastic member comprises a contact portion which is brought into contact with the substrate, and a circumferential wall extending upwardly from the contact portion and connected to the vertically movable member. The circumferential wall has a stretchable and contractible portion which is stretchable and contractible vertically.