Abstract: A damping device for a gun barrel (1) having a muzzle brake (2) comprises a recoil brake (3) and a vibration damper (9) to prevent natural vibrations in the gun barrel when firing a shot, from propagation to the recoil brake. The connection of the vibration damper to the recoil brake (3) and the gun barrel breech (5) is such that the force transfer coupling between the breech and the recoil brake is reduced with respect to said natural vibrations. The vibration damper (9), which may take the form of a column of Belleville springs (10) is dimensioned so that the damping device as a whole has a rigidity substantially less than the recoil brake alone and forms a vibratory system with a natural frequency substantially lower than the frequency of said natural vibrations of the gun barrel when firing a shot.