PURPOSE: To obtain reduction of motor capacity and compact structure of a flying shear in a rolling line of linear materials such as bar steel by providing a cutter shaft and an eccentric shaft which are, respectively, driven by individual driving devices electrically connected to each other through a control unit.

CONSTITUTION: A cutter shaft 6 is steadily rotated by a cutter rotor M1 and held by an eccentric shaft 2 at such a position as to keep a cutter 7 from contact with linear material 12. On the cutting, a control unit not shown generates such a starting command to an eccentric shaft driving motor M2 that an eccentric bore 4 and cutter 7 simultaneously come nearest to the path line to rotate the eccentric shaft 2. Then, after a predetermine period of time, the eccentric bore 4 comes nearest to the path line of the linear material 12, and the tip portion of the cutter 7 comes nearest to the linear material 12 to cut the same. This construction permits reduction of motor capacity, compact structure and increased degrees of freedom of design.