Ethylene vinyl acetate (EVA) copolymers with different amounts of vinyl acetate were melt-functionalized with maleic anhydride. The effect of benzoyl peroxide, t-butyl perbenzoate, and dicumyl peroxide (DCP) as free-radical initiators on the functionalization performance was studied. The crosslinking reactions occur to a larger extent than in polyethylene, indicating that the vinyl acetate groups favor the formation of free radicals. From all the experiments performed in this study, the recommended initiation system to achieve the best values of the functionalization degree and the lower gel content involves the use of DCP in a concentration of about 0.3 wt % and a maleic anhydride concentration around 5.0 wt %. From FTIR and TGA analyses, it is suggested that the hydrogen abstraction in the EVA copolymers occurs both in the methyl group of the acetate moiety and in the tertiary C-H. The free radicals generated in the tertiary C-H react with maleic anhydride in a higher proportion.