A stream of square folded sheets, wherein one marginal portion is thicker than the marginal portion which is parallel thereto, is fed into the nip of a rotary core and one or more flexible bands which are being convoluted onto the core whereby the sheets form a roll having convolutions which alternate with the convolutions of the band or bands. The thicker marginal portions of the sheets are fed in a direction at right angles to the axis of rotation of the core so that, in the absence of any undertaking to the contrary, the diameter of the respective end face of the roll would exceed the diameter of the other end face which is formed by the thinner marginal portions of the sheets. The development of such frustoconical roll is prevented by moving the single band or one of several bands close to that end face of the roll which is formed by the thicker marginal portions of the sheets and by maintaining the thus positioned band under requisite tension in order to compress the thicker marginal portions. The difference between the thicker and thinner marginal portions of the sheets can be monitored and the position(s) of one or more bands can be adjusted in automatic response to detection of the difference.