A wafer holding apparatus for holding a wafer having undulation. The wafer holding apparatus includes a holding portion having a holding surface for holding the wafer, the holding portion being composed of a plurality of piezoelectric elements having suction holes selectively connected to a vacuum source, the piezoelectric elements having front end surfaces collected to form the holding surface. The wafer holding apparatus further includes a frame member supporting the holding portion and a control unit controlling a voltage to be applied to each of the piezoelectric elements according to the undulation of the wafer, whereby the wafer is held on the holding surface in the condition where the undulation of the wafer is followed by undulation produced on the holding surface due to a change in a length of each of the piezoelectric elements.