An assembled media line including a media line, at least one first line connector and at least one first sheathing system, where the media line has a first end and a second end and where the at least one line connector is connected to one of the first and the second end of the media line and the at least one first sheathing system at least partially surrounds the media line, which media line is not dimensionally stable. A contour shaping cap device including at least two parts which together build, at least in sections, a media line surrounding sheath for contour shaping the media line, where the at least two parts are generally bending resistant and have elements for connecting them to one another.