Abstract: The sizing part of the wrapping mechanism in a cigarette rod making machine has a channel-shaped member with a guide surface extending between a straight edge and a U-shaped edge and composed of an infinite number of straight lines each of which connects a point on one of the edges with a point of the other edge. The channel-shaped member cooperates with a tongue whose sides define with the adjacent mutually inclined sections of the guide surface two gaps of constant width for the passage of the marginal portions of garniture tape which is used to drape the web of cigarette paper or other wrapping material around a filler of tobacco or filter material.