PURPOSE: To lap-finish a cylindrical surface, by providing spiral grooves on the cylindrical surface of a jig which is fitted at a small clearance in the surface to be machined and by causing relative rotation between the workpiece and the jig to circulate lapping liquid along the cylindrical surface of the workpiece.

CONSTITUTION: A cylindrical workpiece 1 is secured on the inside surface of a housing 2. A jig 4, which is fitted at a minute clearance in the machined cylindrical surface 10 of the workpiece 1, is supported by bearings 5 on the housing 2 and rotated by a belt 8. Lapping liquid containing abrasive grains of minute diameter is sealed up between seal members 6. When the jig 4 is rotated, the lapping liquid flows in the direction of the axis of the rotation because of spiral grooves provided on the peripheral surface of the jig 4, so that the liquid circulates through the passage 9 of the housing 2 and the opening between the inside surface of the workpiece 1 and the peripheral surface of the jig 4.