A polishing apparatus for polishing a notch portion of a substrate, said apparatus comprising: a rotary holding mechanism configured to hold the substrate horizontally and rotate the substrate; a polishing head configured to bring a polishing tape into sliding contact with the notch portion of the substrate to polish the notch portion; a tape supplying and recovering mechanism configured to supply the polishing tape to said polishing head and recover the polishing tape from the polishing head; a tension sensor configured to measure a tension of the polishing tape; a monitoring unit configured to monitor the tension of the polishing tape based on an output signal of said tension sensor; characterized in that the apparatus comprises an oscillation plate which is coupled to a tilt plate via at least one linear guide, wherein the polishing head is fixed to the oscillation plate; a U-shaped oscillation-receiving block fixed to one end of the oscillation plate; an oscillation shaft having an eccentric shaft; a motor coupled to the oscillation shaft for rotating the same; a bearing mounted on the eccentric shaft, the bearing engaging a rectangular housing space formed in the U-shaped oscillation receiving block; a hollow tilt shaft rotatably supported by bearings (103, 104), wherein the tilt plate is fixed to the hollow tilt shaft and wherein the oscillation shaft extends through the hollow tilt shaft and is rotatably supported by bearings (101, 102) secured to an inner surface of the tilt shaft; and a motor coupled to the tilt shaft for rotating the tilt shaft independent of the oscillation shaft; wherein a rotation of the eccentric shaft is converted into a linear reciprocating motion of the oscillation plate by the linear guide, whereby the polishing head, that is fixed to the oscillation plate, performs a linear reciprocating motion perpendicular to the tangential direction of the wafer, and wherein rotation of the hollow tilt shaft causes rotation of the oscillation plate coupled to the tilt plate via the linear guide thus causing rotation of the polishing head fixed to the oscillation plate. a rotary holding mechanism configured to hold the substrate horizontally and rotate the substrate; a polishing head configured to bring a polishing tape into sliding contact with the notch portion of the substrate to polish the notch portion; a tape supplying and recovering mechanism configured to supply the polishing tape to said polishing head and recover the polishing tape from the polishing head; a tension sensor configured to measure a tension of the polishing tape; a monitoring unit configured to monitor the tension of the polishing tape based on an output signal of said tension sensor; characterized in that the apparatus comprises an oscillation plate which is coupled to a tilt plate via at least one linear guide, wherein the polishing head is fixed to the oscillation plate; a U-shaped oscillation-receiving block fixed to one end of the oscillation plate; an oscillation shaft having an eccentric shaft; a motor coupled to the oscillation shaft for rotating the same; a bearing mounted on the eccentric shaft, the bearing engaging a rectangular housing space formed in the U-shaped oscillation receiving block; a hollow tilt shaft rotatably supported by bearings (103, 104), wherein the tilt plate is fixed to the hollow tilt shaft and wherein the oscillation shaft extends through the hollow tilt shaft and is rotatably supported by bearings (101, 102) secured to an inner surface of the tilt shaft; and a motor coupled to the tilt shaft for rotating the tilt shaft independent of the oscillation shaft; wherein a rotation of the eccentric shaft is converted into a linear reciprocating motion of the oscillation plate by the linear guide, whereby the polishing head, that is fixed to the oscillation plate, performs a linear reciprocating motion perpendicular to the tangential direction of the wafer, and wherein rotation of the hollow tilt shaft causes rotation of the oscillation plate coupled to the tilt plate via the linear guide thus causing rotation of the polishing head fixed to the oscillation plate.