A containment structure for surrounding a rotatable machine includes a double-walled inner shell having a forward end, an aft end, and a substantially cylindrical body extending therebetween. The inner shell includes an inner wall at least partially surrounding a bladed portion of the bladed rotor, and an outer portion that branches radially outward from the inner wall. The containment structure also includes a substantially cylindrical back sheet coupled to the outer portion and disposed radially outward of the inner wall.