A substrate holding apparatus has a substrate holder body with a substrate holding side facing a polishing surface and holding a substrate on the substrate holding side and a retainer ring fixedly secured to the substrate holder body. The retainer ring is arranged to surround an outer periphery of the substrate held by the substrate holder body so that the retainer ring engages with the polishing surface radially outside the substrate as the polishing of the substrate is effected. The substrate holder body is provided with a membrane having inside and outside surfaces. The inside surface cooperates with a surface of the substrate holder body to define a fluid pressure chamber to which a fluid pressure is applied. The outer surface engages with the substrate held by the substrate holder body.