A cutting apparatus is disclosed which is operable to receive a moving feed of material, wherein the material is to be cut into pieces by the cutting apparatus. The cutting apparatus includes a fixed portion over which the material passes, and a rotating portion. The rotating portion includes at least one rolling cutting element that moves in an orbit around the rotating portions axis of rotation when the rotating portion rotates. The orbit of each cutting element is at an angle to the direction in which the material passes over the fixed portion. For at least part of each revolution, each cutting element contacts the fixed portion and rolls along or relative to the fixed portion thereupon cutting the material passing over the fixed portion.
