An internal gear shaving machine 1 which brings a shaving cutter 3 and an internal gear held by a workpiece chuck 2 into engagement with a crossed axes angle, and subjects the tooth flanks of the internal gear to final machining while it rotationally drives at least one of the shaving cutter 3 and the workpiece chuck 2. The workpiece chuck 2 and shaving cutter 3 are supported movably toward and away from each other in a vertical direction with the workpiece chuck 2 higher and supported movably in the horizontal direction relative to each other. The workpiece chuck 3 is constituted to hold the outer circumferential surface of the internal gear with the axis of rotation of the internal gear oriented in a up-down direction so that shavings produced during processing by the shaving cutter can fall downwardly from the internal gear.