In at least one embodiment, for producing segments of tubular jackets, a strip-shaped sheet material is continuously reshaped transverse to the strip axis into a closed form and following the welding of a longitudinal seam, jacket sections are cut off the jacket strip. In at least one embodiment, a support edge is provided on the inside of the continuously formed jacket strip for the cutting operation, essentially in the form of a closed circle and extending in a normal plane to the longitudinal axis of the jacket strip, which fits directly against the inside of the jacket strip and cooperates with at least one cutting tool. The cutting tool is pivoted into the cutting position during the cutting operation along the support edge, so that a cutting region rotates once around the longitudinal axis. A section of the jacket strip is cut off, wherein during the cutting operation, the support edge and the at least one cutting tool are advanced along with the jacket strip. Following the cutting operation, the at least one cutting tool is moved to a non-contacting position relative to the support edge and together with the support edge is moved counter to the movement of the jacket strip and back to the starting position occupied prior to the cutting operation.