PURPOSE: To prevent chipping of cutter while to improve the cutting efficiency of hard-to-cut material or general steel member and the service life of saw cutter by varying relative cutting speed of saw cutter and material to be cut continuously and periodically with correspondence to the material to be cut.

CONSTITUTION: When moving a section for holding a band saw cutter 9 for lateral band saw machine 1 by means of a moving mechanism 19 and performing cutting, SOL2 of solenoid valve 29 is excited to exchange said valve 29 to the left position thus to feed pressure oil from hydraulic pump 25 through conduits 27, 45 into pilot operation check valve 47 and to open said valve 47. Consequently, the saw cutter holding section 13 will start lowering of band saw 9 through self-weight while pressure oil in cylinder pressurized through lowering of piston 41 in moving mechanism 19 is returned through conduit 39, said valve 47, conduit 49, reducing valve 51 and motor flow regulation valve 55 into a tank T. At this time, rotation of motor of flow regulation valve 55 is controlled to vary oil flow continuously or periodically.