PURPOSE: To prevent the occurrence of oblique cutting through horizontal clamping even when a material to be cut is short by vertically moving a slide plate according to vertical movement of a vise bed, in a vise devise used for a band sawing machine.

CONSTITUTION: A vise jaw 9 on the stationary side of a vise device is coupled integrally with a vise bed 27 and integrally has a slide plate 29 horizontally extending between a vise jaw 11 on the moving side and the vise jaw on the stationary side. The vise bed 27 is vertically movable. Thus, since the slide plate 29 is vertically moved through vertical movement of the vise bed 27, the slide plate 29 is positioned in the same level as that of a conveyance line for a material M to be cut during clamping. As against the above, during unclamping, the slide plate 29 is lowered to a level lower than that of the conveyance line. As a result, the slide plate 29 supports the material M to be cut in the same level as that of the conveyance line without impeding conveyance of the material to be cut.