A purpose of the disclosed method is to impart gathers and elasticity to a relatively inelastic film, membrane, or web substrate, through elastic banding with a viscoelastic hot melt pressure-sensitive adhesive (PSA). Typically, the resulting elastic-banded substrate product (e.g. 40) will be cut into discrete units and formed into garments or body-encircling members such as disposable diapers. One step of the preferred method involves extruding a ribbon or band (13 or 113) comprising a viscoelastic hot melt PSA, which PSA has unusually high cohesion, stretchiness, and elasticity without excessive loss of adhesive bonding strength. (The viscoelastic behavior of the PSA is believed to be determined, at least in part, by the relative size of its crystalline domains and its rubbery domains and the glass transition temperatures and softening points of its components.) A second step of the preferred method involves bringing the band of hot melt (13 or 113) into adherent contact with a surface of a moving continuous substrate (22 or 32 or 132). A typical substrate would be the polyolefin film used in the manufacture of disposable diapers. The band can be bonded to the substrate through a pressure activation technique, wherein the band itself has the necessary inherent adhesive properties.