An elastic bandage is disclosed having a nonelastic absorbent nonwoven web, a non-elastic breathable nonwoven web, and a meltspun elastomeric material disposed between the two webs. The meltspun elastomeric material can comprise a plurality of meltspun elastomeric filaments aligned in substantially parallel distribution in a machine direction, the filaments attached to a side of the nonelastic breathable nonwoven web and to a side of the nonelastic absorbent nonwoven web. The nonelastic absorbent nonwoven web can comprise a laminate of nonwoven layers. The non-elastic breathable nonwoven web can comprise a breathable film bonded to a nonwoven layer or laminate individual nonwoven layers. A self adherent coating may be disposed upon an outer surface of the elastic bandage.