PURPOSE: To extend the useful life of a band saw and increase cutting efficiency by applying the uniform-speed tangential shift type seesaw motion so that no unreasonable load is applied to the band saw.

CONSTITUTION: A pair of push-pull motion means 10a, 10b connected to a band saw support frame 9 are pushed or pulled respectively for repeated operations. Drive directions are reversed to each other, and the drive speed in the approaching direction to a cut material is gradually decreased, and the drive speed in the leaving direction from the cut material is gradually increased. Accordingly, the uniform-speed tangential shift type seesaw motion is applied to a band saw supported by the frame 9. At positive and reversed stroke ends of the seesaw motion, a relative approach shift by a predetermined quantity is performed, thereby the cut material cn be circularly cut at a fixed thickness via the fixed cutting length and the fixed circular cutting speed.