A composite tube for a gun barrel and a method for making the tube are disclosed. The tube includes a plurality of elongate carbon fibers and a resin material surrounding a longitudinal bore axis. The elongate carbon fibers are aligned parallel with the longitudinal bore axis and are under compression along the longitudinal bore axis. Such a tube for a gun barrel may be made by wrapping a tubular metal liner with a resin matrix material containing a plurality of elongate carbon fibers, and aligning the carbon fibers parallel with the longitudinal axis of the liner. The resin matrix material is cured, and the elongate carbon fibers are placed under compression along the longitudinal axis of the liner. Compressing the carbon fibers along the longitudinal axis of the liner produces a tube of surprising stiffness. The tube provides a highly stable gun barrel of reduced weight for good accuracy.