PURPOSE: To improve a degree of rigidity as a whole and prevent a vibration from occurring as well as to perform such cutting as being excellent in accuracy, by making one end side of a head rotatably supportable on a base body of a band sawing machine by means of a pivoted shaft, while having the other end side coupled by a hydraulic cylinder.

CONSTITUTION: Inside a head, there are provided with wheels 2 and 3 at both sides, while a band saw is rolled round in space between both these wheels in an endless way. As for the head 1, its one end side is rotatably supported on a base body 9 by means of a pivoted shaft 1a while the other end side is rotatably coupled in space between the head and the base body 9 via a hydraulic cylinder 10. Therefore, vibrations in the head and a saw blade are well damped so that rigidity in the whole lot of the band saw is remarkably improved.