A polishing apparatus comprises a polishing member that has a wide stable polishing range to perform effective polishing, even if a rotation axis moves away from the edge of a workpiece. A polishing member holder holds the polishing member, and a workpiece holder holds the workpiece to be polished. A drive device produces a relative sliding motion between the polishing member and the workpiece. At least one holder of either the polishing member holder or the workpiece holder is rotatable about a rotation axis and is tiltable with respect to other holder. Such one holder is provided with a pressing mechanism to stabilize orientation or desired posture of the one holder by applying an adjusting pressure to the one holder at a location away from the rotation axis.