Distinctive features of free-radical grafting of trans-ethylene-1,2-dicarboxylic acid (TEDA) onto macromolecules of molten ethylene-vinyl acetate copolymer (EVA) in the course of reactive extrusion have been investigated along with structure, mechanical characteristics, and high-elastic properties of molten functionalized products (EVA-g-TEDA). It is shown that EVA-g-TEDA yield depends on both the peroxide initiator concentration and content of vinyl acetate units in the copolymer molecular structure. At functionalization, acid grafting is accompanied by secondary reactions of macromolecular degradation and crosslinking. With a low-peroxide initiator concentration (0.1 wt %), degradation prevails; with a higher (0.3 wt %) concentration, crosslinking of macromolecules prevails. It is reported that monomers being grafted attach mostly over secondary carbon atoms in the polymer chain. EVA-g-TEDA appears to have a less perfect crystal structure with a lower-melting temperature and crystallinity as against the starting polymer. The functionalized products display enhanced rigidity and lower deformability in comparison with the initial copolymer. Variations in the swelling ratio and melt strength of EVA-g-TEDA depend on the course of competing secondary processes of macromolecular degradation and crosslinking. (C) 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 127: 3104-3113, 2013