A nonwoven web material that includes an elastic component or material (e.g., nonwoven web, nonwoven web laminated to an elastic material, etc.) is provided. The elastic component contains a crosslinked network formed from a pentablock copolymer containing at least two monoalkenyl aromatic midblocks positioned between conjugated diene endblocks, such as butadiene-styrene-butadiene-styrene-butadiene (“BSBSB”) or isoprene-styrene-isoprene-styrene-isoprene (“ISISI”). Prior to crosslinking, the pentablock copolymers have a relatively low viscosity and thus may be readily formed into a precursor elastic material (e.g., film, strands, web, etc.) that is subsequently crosslinked to achieve the desired elastic and mechanical properties.