A composite tube for a gun barrel consists of: an inner tubular metal liner defining a longitudinal bore axis; a resin matrix material surrounding the liner, the resin matrix material containing a plurality of elongate carbon fibers, the carbon fibers being aligned parallel with the longitudinal bore axis of the liner and under compression along the longitudinal bore axis; a muzzle piece attached to the muzzle end of the barrel; and a breech piece attached to the breech end of the barrel, so that any vibrations transmitted along the longitudinal bore axis of the liner are absorbed by the resin matrix material and so that any vibrations reaching the muzzle piece and breech piece are reflected back into the resin matrix material and thus absorbed. A method of manufacturing the composite tube for a gun barrel consists of the steps of: a) grinding the metal liner down from its original thickness to a greatly reduced thickness; b) applying the resin matrix material in layers about the metal liner by wrapping a carbon fiber mat with embedded resin about the metal liner under extreme pressure, until a suitable thickness of resin matrix material has been applied to the metal liner; c) compressing the wrapped resin matrix material; d) heating the wrapped resin matrix material and enclosed metal liner while maintaining compression on the resin matrix material to cure the resin matrix material; e) lathing and sanding the cured resin matrix material to the proper diameter for a gun barrel; and f) attaching the muzzle piece and breech piece to the gun barrel with the adhesive material.