A bandsaw machine which has a sawhead assembly in which a flexible endless bandsaw blade is trained around a pair of bandsaw blade wheels to cut a workpiece, with the blade being guided by a guide arm, includes a guide member on the guide arm, for holding the bandsaw blade in a vertical orientation by pushing the bandsaw blade from both sides. A rolling member is mounted on the sawhead assembly and is free to push a side surface of the bandsaw blade with a predetermined force so as to prevent vibration of the blade.