Elastic films are commonly incorporated into products (e.g., diapers, training pants, garments, etc.) to improve their ability to better fit the contours of the body. For example, an elastic composite may be formed from the elastic film and one or more nonwoven web facings. The nonwoven web facing may be joined to the elastic film while the film is in a stretched condition so that the nonwoven web facing can gather between the locations where it is bonded to the film when it is relaxed. The resulting elastic composite is stretchable to the extent that the nonwoven web facing gathered between the bond locations allows the elastic film to elongate. Styrenic block copolymers are often employed to form the elastic film of such composites that contain a conjugated butadiene block positioned between two styrene blocks (i.e., S-B-S). Unfortunately, such polymers are often difficult to process into a film due to their relatively high viscosity. As such, a need exists for a material that may be formed from a low viscosity polymer, yet exhibit good elastic performance during use.