The present invention is directed to improved elastic materials. More specifically, the present invention is directed to low basis weight elastic webs, such as elastic films and elastomeric fibrous meltblown or spunbond webs which may include elastomeric fibers and/or elastomeric continuous filaments. The present invention is also directed to laminate structures which include the elastic webs. The elastic webs include an elastomeric block copolymer and a polyolefin wax, and do not include a tackifier. The low basis weight elastic webs of the present invention may display tension values upon elongation equal to or greater than the tension values of previously known elastic webs of greater basis weight. The elastic laminate structures of the present invention comprise at least one layer an elastic web adhesively bonded to one or more other webs, such as, for instance a woven or nonwoven web. The elastic laminate structures made in accordance with the invention have shown remarkably good uniformity, hand, bulk, strength and elastic properties while decreasing the required amount of raw materials. In addition, the individual layers of the disclosed laminate structure may shown improved compatibility with each other and may display improved bonding between layers.