Abstract: A hollow, tube-shaped ball bat having a damping core made a tube of brass wrapped in a resilient sleeve made from polystyrene closed cell foam is disclosed. The damping core is forcibly inserted into the interior of the hollow bat by compressing the resilient sleeve. When assembled into the bat, the resilient sleeve is under great compression. Furthermore, the tubing wall forming the bat is relatively thin to transmit the impact of the ball to the resilient sleeve. The processes to obtain a damped core bat are also disclosed. A tube is provided which is swaged to form a barrel portion, a tapered portion, and a handle portion. The resilient sleeve is compressed and inserted into the open top of the tube. Alternatively, the damping core is inserted into the tube and the inner damper which has a tube structure is expanded radially to compress the resilient sleeve between it and the tube wall. The top of the tube is covered by a cap and the bottom of the tube is enclosed with a knob.