A one-piece barrel assembly cart includes a right assembly cart base connected with a left assembly cart base and at least three stabilizer rings that are attached to the assembly cart base. The one-piece barrel assembly cart may be used to stabilize a tapered cured composite barrel, for example the large fuselage barrel of the aft section of a large new generation aircraft, such as a 7E7 Boeing airplane. A modular assembly cart includes at least two identical modules. Each of these modules includes a cart base and a stabilizer ring. The diameter of the inner surface of the stabilizer ring may vary as needed. Other modules including a fuselage support may be added. By providing modular assembly carts any shape and size of a one-piece composite barrel may be stabilized after curing of the composite material.