A polishing apparatus for polishing a substrate comprises a polishing table having a polishing surface, and a substrate holding apparatus for holding a substrate to be polished and pressing the substrate against the polishing surface. The substrate holding apparatus comprises a vertically movable top ring body for holding a substrate, and a fluid supply source for supplying a fluid under a positive pressure or a negative pressure to a hermetically sealed chamber which is defined in the top ring body so as to control pressure under which the substrate is pressed against the polishing surface. The substrate holding apparatus further comprises a measuring device disposed in a fluid passage interconnecting the hermetically sealed chamber and the fluid supply source for measuring a flow rate of the fluid in the fluid passage.