A method of forming reinforced bags, comprising: feeding a web of bag material (M, M') along a first path of travel (27, 202); folding the web of bag material (M, M') to form a sleeve; forming perforations, score lines, cuts, or lines of separation (35, 223) for forming a series of bags moving along the first path of travel (27, 202); feeding a series of reinforcing elements (10, 10') along a second path of travel (60, 243) toward registration with the bags, each reinforcing element (10, 10') comprising a central body section (11, 11'), a first peripheral side portion (13A, 13A') foldably connected to the central body section (11, 11'), and a second peripheral side portion (13B, 13B') foldably connected to the central body section (11, 11'), wherein a first lock zone (19A, 19A') extends from a first fold line (17A, 17A') extending in the central body section (11, 11') to a second fold line (18A, 18A') extending in the first peripheral side portion (13A, 13A'), and a second lock zone (19B, 19B') extends from a third fold line (17B, 17B') extending in the central body section (11, 11') to a fourth fold line (18B, 18B') extending in the second peripheral side portion (13B, 13B'); applying a first adhesive material (12, 12') to the central body section (11, 11') of each of the reinforcing elements (10, 10') in a desired pattern sufficient to securely adhere each reinforcing element (10, 10') to a corresponding bag of the series of bags, wherein the first adhesive material (12, 12') extends in the central body section (11, 11') along the first fold line (17A, 17A') and the third fold line (17B, 17B'); moving the reinforcing elements (10, 10') into adhesive contact with their corresponding bags; applying a second adhesive material (12, 12') to the first peripheral side portion (13A, 13A') and the second peripheral side portion (13B, 13B') of each of the reinforcing elements (10, 10') after the moving the reinforcing elements (10, 10') into adhesive contact with the bags, the first lock zone (19A, 19A') and the second lock zone (19B, 19B') being generally free of the first adhesive material (12, 12') and the second adhesive material (12, 12') to enable each reinforcing element (10, 10') to support their corresponding bags in an opened configuration, wherein the second adhesive material (12, 12') extends in the first peripheral side portion (13A, 13A') along the second fold line (18A, 18A') and in the second peripheral side portion (13B, 13B') along the fourth fold line (18B, 18B'); and folding peripheral portions (13A/13A', 13B/13B') of the reinforcing elements (10, 10') about their corresponding bags to secure the reinforcing elements (10, 10') in an enclosed position thereabout; wherein the adhesive material (12, 12') extends substantially across the width of the reinforcing elements (10, 10'). feeding a web of bag material (M, M') along a first path of travel (27, 202); folding the web of bag material (M, M') to form a sleeve; forming perforations, score lines, cuts, or lines of separation (35, 223) for forming a series of bags moving along the first path of travel (27, 202); feeding a series of reinforcing elements (10, 10') along a second path of travel (60, 243) toward registration with the bags, each reinforcing element (10, 10') comprising a central body section (11, 11'), a first peripheral side portion (13A, 13A') foldably connected to the central body section (11, 11'), and a second peripheral side portion (13B, 13B') foldably connected to the central body section (11, 11'), wherein a first lock zone (19A, 19A') extends from a first fold line (17A, 17A') extending in the central body section (11, 11') to a second fold line (18A, 18A') extending in the first peripheral side portion (13A, 13A'), and a second lock zone (19B, 19B') extends from a third fold line (17B, 17B') extending in the central body section (11, 11') to a fourth fold line (18B, 18B') extending in the second peripheral side portion (13B, 13B'); applying a first adhesive material (12, 12') to the central body section (11, 11') of each of the reinforcing elements (10, 10') in a desired pattern sufficient to securely adhere each reinforcing element (10, 10') to a corresponding bag of the series of bags, wherein the first adhesive material (12, 12') extends in the central body section (11, 11') along the first fold line (17A, 17A') and the third fold line (17B, 17B'); moving the reinforcing elements (10, 10') into adhesive contact with their corresponding bags; applying a second adhesive material (12, 12') to the first peripheral side portion (13A, 13A') and the second peripheral side portion (13B, 13B') of each of the reinforcing elements (10, 10') after the moving the reinforcing elements (10, 10') into adhesive contact with the bags, the first lock zone (19A, 19A') and the second lock zone (19B, 19B') being generally free of the first adhesive material (12, 12') and the second adhesive material (12, 12') to enable each reinforcing element (10, 10') to support their corresponding bags in an opened configuration, wherein the second adhesive material (12, 12') extends in the first peripheral side portion (13A, 13A') along the second fold line (18A, 18A') and in the second peripheral side portion (13B, 13B') along the fourth fold line (18B, 18B'); and folding peripheral portions (13A/13A', 13B/13B') of the reinforcing elements (10, 10') about their corresponding bags to secure the reinforcing elements (10, 10') in an enclosed position thereabout; wherein the adhesive material (12, 12') extends substantially across the width of the reinforcing elements (10, 10').