PURPOSE: To perform the accurate cutting along an ideal cut line, and prevent generation of non-conforming product and lowering of the working efficiency in a band sawing machine by always monitoring a displacement quantity of a band saw blade positively, and correcting it.

CONSTITUTION: An endless band saw blade 7 is stretched between a driving and a driven wheels 6a, 6b for travelling, and detecting means 27, 28, 29, 30 for detecting displacement quantity in the cross sectional direction of the band saw blade 7 in a linear travelling part (a) and a position adjusting means for adjusting a position of the linear travelling part (a) are provided in a band sawing machine for cutting a work W in the liner travelling part (a) thereof. Operation control of the position adjusting means is performed by the output signal of the detecting means 27-30. Position of the linear travelling part (a) is adjusted by turning the band saw blade 7 around of the blade tip thereof in the cross sectional direction. Curved sawing is therefore restrained to perform the accurate cutting.