Abstract: Apparatus for providing rolls of convoluted paper or the like with cylindrical envelopes defines an elongated path wherein the rolls are advanced sideways first to a centering station where the end faces of successive rolls are overlapped by inner discs which are attached to the rolls by plugs extending into the end portions of central openings provided in the cores of the respective rolls. The rolls are thereupon advanced to a draping station where they are set in rotary motion and provided with blanks of wrapping paper whose marginal portions are folded over the outer sides of the inner discs before the rolls advance to a pressing station where the folded-over marginal portions of the blanks are compressed against the outer sides of the inner discs and, at the same time, the pressing plates of the pressing device apply outer discs to the folded-over marginal portions to thus complete the making of cylindrical envelopes for the respective rolls.