A cross-linked polymeric composition comprises a linear, low density ethylene homo- or copolymer which, prior to cross-linking is characterized by (a) a density at 25.degree. C. of 0.940 gm/cm.sup.3 or less (b) a linearity expressed in terms of pendant methyl groups per 10.sup.3 carbon atoms of the polymeric chain of less than 30 with a substantial absence of long chain branches, and preferably (c) no more than 5 branches greater in length than C.sub.8. The cross-linked polymeric composition is particularly suitable for the production of dimensionally recoverable articles, for the production of insulation material, for the production of semi-conductive or conductive polymers for use in electrical heating materials, and for the production of semi-permeable membranes.