Embodiments of the present invention are improved targets suitable for cutting with an edged weapon. In an embodiment the target may be a traditional straw mat target held together by a hydraulic binder composition. In yet other embodiments, the target may be made of multiple layers of synthetic materials to give different properties. One embodiment is a target with an inner portion and an outer portion. The outer portion may be selected from a material that gives the appropriate initial cutting properties while the inner portion provides a cutting resistance. In addition, shaped targets having multiple differing cutting surfaces are disclosed, as is a method for creating a target to simulate a predefined sequence of cuts.