A flexible traction organ that can be wound and unwound, in particular for passenger and/or goods lifts, said organ comprising at least one stranded cable consisting of a tensile resistant material. The core strand of each stranded cable is surrounded by a flexible thermoplastic plastic layer. A production line for embedding several stranded cables in a flexible thermoplastic layer comprises a respective reel for unwinding the stranded cable, a device for accurately aligning the stranded cable, a heating element for pre-heating the stranded cable, at least one extruder for co-extruding the stranded cable in a flexible plastic sheathing, a cooling vat, a reel storage unit, a cutting unit and a reserve reel. The extruder, a wire guide and at least one die can be adjusted individually, conjointly and in relation to one another on a plane (P) that runs at an angle to the cable plane (E). The unwound stranded cables are degreased and/or pre-treated to improve the adhesion of the plastic sheathing, and pre-heated to a temperature of approximately ±20° C. in relation to the melting temperature of the flexible, thermoplastic plastic that surrounds the core strand and are sheathed with liquefied plastic in the extruder.