To finish a workpiece material in a uniform grinding amount and grinding surface even when it has variation in thickness.

A side grinding belt sander machine, having a sanding head in at least one side of a material feed passage 3, is provided with a thickness detector detecting a thickness of a workpiece material, central control unit assigning transmitting force by thickness information from the thickness detector so as to provide a relation between a thickness t of the workpiece material and the transmitting force F in almost direct proportion, output generating means of a profile cylinder or the like generating the transmitting force F instructed from the central control unit, and a sanding roller bringing the sanding head into press contact with a side of the workpiece material by the transmitting force generated from the output generating means. Since the thickness of the applied workpiece material w and the transmitting force F are placed in a relation of almost direct proportion, almost an equal tread pressure p always acts in a side of the workpiece material w, an excellent effect capable of obtaining a uniform grinding amount is provided.