The Gothic arch groove profiles are used in linear ball bearings as guide tracks for the rollers. After grinding the grooves are finished with a fine stone. The stone (10) swings in the groove (7) about an axis which is aligned at an angle to the line of the groove. In addition to the swinging motion of the stone, it is moved axially in the direction while the nut (6) is rotated about the axis so that the stone traveres the groove. - As the stone swings e about axis it simultan-eously finishes both sides of the groove on the oblique section. The projection on the normal cross-section of the groove is an ellipse which approximates closely to the desired profile. ADVANTAGE- Simultaneous finishing of whole groove profile. Greater accuracy and better surface finish. (4pp Dwg.No.1/13)