Abstract: A device for finishing shaped surfaces with an abrasive tool comprises a fixed base connected to a copying mechanism having a reciprocating carriage moving on the fixed base and carrying a double-arm lever pivotally mounted on a spherical bearing. Secured on one arm of the lever is an abrasive tool performing periodic swivelling motion about its own axis from a turning mechanism. The abrasive tool is urged to the surface being mechined by means of a hold-down member operatively connected with the second arm of the lever, the axis of the hold-down member passes through the center of the spherical bearing of the lever. The device of the present invention ensures an effect of urging of the tool in any point of the surface of intricate shape being machined.