The creasing rules customarily carried by the die roll of a rotary die apparatus are quite narrow and project only a limited distance beyond the arcuate outer surface of the die board of the die roll. Due to the highly localized nature of the forces imposed upon the paperboard material by the narrow rules, they frequently cut and/or crack the paperboard material, instead of merely forming a crease or fold line. The crease or fold line formed by the rule is of course of correspondingly narrow width. Consequently, when sections of the paperboard material upon opposite sides of the fold line undergo relative pivotal movement toward each other, they quickly abut and resist further pivotal movement. This may and likely will cause the fold line to "wander," rather than being substantially straight, and/or may cause the presence of "phantom" fold lines that are spaced laterally from and that extend generally parallel to the intended fold line. Cutting and cracking of the paperboard material, wandering of the intended fold line and the creation of phantom fold lines each may weaken the strength of the paperboard material and/or may result in improper folding of the sections of the paperboard material upon opposite sides of the fold lines. This in turn causes the production of defective cartons or boxes from the paperboard material.