A substrate holding apparatus and a polishing apparatus which can reduce vibrations of a top ring in its entirety by damping vibrations transmitted from a retaining ring to a top ring body is disclosed. The substrate holding apparatus includes a top ring body having a substrate holding surface configured to hold and press a substrate against a polishing surface, a retaining ring configured to surround the substrate and to contact the polishing surface, and a drive ring comprising a ring member configured to hold the retaining ring on a lower surface thereof, a central member disposed at a central part of the top ring body and supported by the top ring body, and a connecting portion configured to connect the ring member and the central member. The drive ring includes a first material and a second material having a modulus of longitudinal elasticity smaller than the first material.