Based on the relations among the stress, final wall-thickness of thin-walled tube and the characteristics of tube material, original size, curling radius along with friction condition in a axially-compressed internal inversion process on right-angled fillet die, some analytical discriminants were established for judging if a double-layered tubular piece of aluminum alloy could be steadily formed from a certain-sized round tube via internal inversion process without interference and plastic instability of tube wall, and a method was put forward for determining the maximum and minimum usable curling radius or die fillet-radius for thin-walled tubes in the process. Analysis shows that choosing tube material with little Bauschinger effect and decreasing the friction coefficient between tube and die will help to improve the formability of tubes in the process and enlarge the usable range of curling radius. The analytical conclusions aiming at the performance of two kinds of aluminum alloy tube in the process are in good accordance with the acquirable experimental results in some references.