Abstract: An improved rotary pressure cutting apparatus that cuts, perforates, and scores plies of paper, window materials, label stock, and plastic laminates in conjunction with soft, discontinuous, and/or non-cylindrical anvil surfaces. A light weight, low mass anvil in the form of a metallic sheet is supported in a strike position beneath a rotating blade. The anvil is biased by springs or elastomeric members toward the strike position and moves with the material being cut and the moving cutting blade during a cut. The anvil is returned to the strike position by the biasing member upon completion of the cut.