Abstract: A laminated composite suitable for use in medical products such as tapes and wraps. The composite includes, for example, a first nonwoven fiber layer, an elastic layer, a melt blown adhesive fiber layer, and a second nonwoven fiber layer. A scrim layer serves as a deadstop, or stretch limit, to prevent over stretching. The non-woven fiber layer(s) and/or the scrim layer form suitable loops for a hook and loop fastening system. The scrim layer in some embodiments is employed to make the composite finger tearable. The melt blown adhesive layer, nonwoven web layer and elastic layer form a breathable, porous elastic composite. Methods of manufacturing the composite are also disclosed.