A roll tensioner for use in maintaining a wrapping material cut edge of a wrapping material retained on a wrapping material roll located within a wrapping material box having an interior cavity with an interior front wall with a top cutting edge. The roll tensioner comprises a thin, flexible main body having distal and proximal end sections separated by a spring back reversion section, and formed having a first side and a second side. Attachment means, preferably an adhesive, is located on at least a portion of the proximal end section on the first side adapted to attach the proximal end section to the interior front wall of the wrapping material box. The spring back reversion section is composed of a material that has an immediate elastic response to a static load and is capable of substantially full recovery when the static load is removed. The distal end mechanically bends downward by way of the spring back reversion section in the interior cavity of the wrapping material box. The distal end section is adapted to rest against the wrapping material proximal to the wrapping material cut edge to retain the wrapping material cut edge in an upward, substantially parallel position to the interior front wall of the wrapping material box for easy grasping of the wrapping material cut edge by an end user.