An elastic membrane is used in a substrate holding apparatus for holding a substrate such as a semiconductor wafer and pressing the substrate against a polishing surface. The elastic membrane includes a plurality of concentrically circumferential walls configured to define a plurality of pressurizing areas for pressing the substrate. The pressurizing areas includes a central pressurizing area located at a central part of the elastic membrane, an annular edge pressurizing area located at the outermost part of the elastic membrane, and a plurality of intermediate pressurizing areas located between the central pressurizing area and the annular edge pressurizing area. The area width of at least one of the intermediate pressurizing areas is set in a range to allow a polishing rate responsive width not to vary even when the area width is varied.