The present disclosure relates to removable, nonslip, non-adhesive coverings which are used as shelf, drawer or storage liners. In particular, the covering sheet features an improved composite material having a top decorative layer of flocked polymeric film combined to a continuous bottom layer of unsupported foam. The structure of the multilayered composite material facilitates the convenient hand tearing of the sheet to size through a grid of perforations that are obscured by a fine coating of natural or synthetic fibers.