According to known techniques for winding an ammunition shell the number of thread layers is often reinforced as compared to the remaining part of the shell wall, especially in those zones of the shell where the load is the highest, thereby, however, inevitably increasing the thickness of the shell wall. If the space for the propelling charge in the wound shell is to be enlarged while the outer geometry of the wound shell remains the same, that is with the same space provided in the weapon for the charge, the wall thickness has to be reduced. In order to provide the shell with the same mechanical stability, despite the reduction in wall thickness, as shells whose wall thickness is not reduced, the wound body of the shell (50) is produced from chemical fibers (53), preferably from synthetic and inorganic chemical fibers.