Abstract: A tensioning device for tensioning the plastic band. The device has a tensioning element which can be rotated about an axis and has a flat gripping region. A clamping element is also mounted such that it can be rotated about the axis and, when the tensioning element is in the inoperative position, is supported against a stop. In this position, the plastic band can be moved freely between the gripping surface of the clamping element and the tensioning element. To tension the plastic band, the tensioning element is rotated in the tensioning direction and the gripping region of the tensioning element is thereby moved against the gripping surface so that the plastic band is held in a planar manner. With the plastic band being held, the gripping region, as seen in the tensioning direction and with respect to the axis, is inclined inwardly in the radial direction. During further rotation of the tensioning element the plastic band which is clamped between the tensioning element and the clamping element is tensioned.