A rotary die cutter is provided having a knife cylinder, provided on its peripheral surface with a punching blade, and an anvil cylinder around which is wound an anvil against which the punching blade is urged in punching material from cardboard passing between the knife cylinder and the anvil cylinder. The cylinders are driven by meshing gears disposed at the ends of the cylinders and having different numbers of teeth. A pair of helical gears are disposed at one end of the anvil cylinder. One of these helical gears is attached to the anvil cylinder and the other is connected to one of the meshing gears. A mechanism is provided for causing axial movement of the anvil cylinder. This axial movement is converted into rotational movement of the anvil cylinder by the relative movement of the helical gears. As a result, the positional relationship between the punching blade of the knife cylinder and the outer peripheral surface of the anvil cylinder is successively changed to avoid local concentration of the impressions of the punching blade in the anvil surface and thereby to insure longer anvil life.