A scoring or cutting assembly forms a part of a cutting die used to score and cut corrugated board. The scoring or cutting assembly includes a cutting or scoring rule secured to a die board. First and second elastomers are secured on the die board such that the scoring or cutting rule extends between the elastomers and there is defined a space between the scoring or cutting rule in each of the elastomers. There is also provided a pair of retainers, each retainer being secured to the die board adjacent an outboard side of the elastomers. During a cutting or scoring operation, the elastomers engage the corrugated board on opposite sides of the scoring or cutting rule and apply and inward force to the corrugated board towards the scoring or cutting rule. This causes the corrugated board to resist cracking on opposite sides of the scoring or cutting rule.