Abstract: In the case of weapon barrels which are only secured at one of their ends at the weapon housing during firing of the weapon there occurs, particularly during series firing, bending vibrations or oscillations which impair the hit probability of the fired projectiles. In order to preclude or at least dampen such bending vibrations of the weapon barrel the invention contemplates securing a vibration damping device or damper at the muzzle of the weapon barrel. This vibration damper comprises an inertia body which is resiliently connected with the weapon barrel muzzle. Also provided is a brake device which dampens the movement of the inertia body relative to the weapon barrel. The inertia body preferably comprises two ring members which are pressed by springs against two disc members which are rigidly attached to the weapon barrel muzzle. Between the weapon barrel and the ring members of the inertia body there are arranged resilient elements, such as blade or leaf springs.