There is provided a substrate polishing machine which comprises a polishing surface and a substrate carrier for holding a substrate and bringing it into contact with the polishing surface. The substrate carrier comprises a carrier body, a substrate holding member for holding a substrate with a surface of the substrate to be polished being directed towards the polishing surface. The substrate holding member is mounted on the carrier body in such a manner that the substrate holding member is movable both towards and away from the polishing surface. The substrate polishing machine further comprises a substrate holding member positioning device provided on a side of the substrate holding member opposite to that used for holding the substrate. The substrate holding member positioning device has a flexible member which defines a chamber, and which, upon introduction of a non-compressible fluid, is expanded in a direction towards the polishing surface.