A method of making an elastomeric, hot-melt adhesive foam is disclosed. The method involves melting an adhesive material, mixing a gas with the adhesive material under pressure to form a solution of the gas in the adhesive material, reducing the pressure to cause evolution and/or expansion of the gas to form a foam, and stabilizing the foam by causing the adhesive material to solidify. The relatively low melt-viscosity of the adhesive material which is used to form the foam provides desirable processing times and the ability to form foams having desired physical properties, e.g., caliper and cell structure. The adhesive material of which the foam is comprised preferably comprises: (a) about 15% to about 60%, by weight of the adhesive material, of an A-B-A block copolymer, in which the A block is derived from styrene and the B block is derived from butadiene or isoprene; (b) about 30% to about 70%, by weight of the adhesive material, of an aromatic modified hydrocarbon resin which associates with both the B block and A blocks of the A-B-A block copolymer; and (c) 0 to about 30%, by weight of the adhesive material, of a processing oil. The proportions of the components (a), (b), and (c) are selected such that the elastomeric, hot-melt adhesive material has a viscosity of less than about 200,000 centipoise at 325.degree. F. and an elastomeric retention value of at least 75%. The adhesive material is preferably pressure-sensitive so as to allow lamination of the solified foam comprising the adhesive material with components of absorbent articles without the need for external bonding agents. Also disclosed is a method of elasticizing structures and absorbent articles with the foam. The adhesive foam and structures incorporating same are particularly useful in disposable absorbent articles such as diapers, training pants, incontinent devices, and the like.