Polyethylene aerogels and aerogel fiber webs have a high degree of molecular alignment and interconnected fibers, which offer good mechanical strength and high porosity with open interconnected three-dimensional pore structure of the aerogel fibers. The high porosity of the aerogel fibers forming the web, offer a distinct advantage over solid fibers and fiber webs formed from polymer melts, or other non-gel form of polymer solutions. In this procedure, the polymer in solution is made into cross-linked gel with three-dimensional open pore structure before introducing it to the fiber web making process.