Cross-linked foam structures of essentially linear polyolefines and process for manufacture

New cross-linked polymeric foam compositions, and methods for making the same, are provided. The new compositions utilize novel cross-linked polyolefin copolymers and show improvements in strength, toughness, flexibility, heat resistance and heat-sealing temperature ranges as compared to conventional low density polyethylene compositions. The new compositions also show processing improvements over linear low density polyethylene. The novel polyolefins, which are essentially linear, comprise ethylene polymerized with at least one alpha-unsaturated C3 to C20 olefinic comonomer, and optionally at least one C3 to C20 polyene, and exhibit, in an uncross-linked sense, a resin density in the range of about 0.86 g/cm3 to about 0.96 g/cm3, a melt index in the range of about 0.5 dg/min to about 100 dg/min, a molecular weight distribution in the range of from about 1.5 to about 3.5, and a composition distribution breadth index greater than about 45 percent.