Melt grafting of maleic anhydride onto elastomeric ethylene-octene copolymer was carried out in a twin-screw extruder, in the presence of dicumyl peroxide as an initiator. Dimethyl formamide was used as an inhibitor to reduce crosslinking and as a solvent for peroxide initiator. The aim of the work is to produce the copolymer with reactive functionality without the expense of elastomeric characteristics. Particular consideration was, therefore, given to the effects of initiator and monomer concentrations, and of screw speed on the degree of grafting, percentage of conversion, amount of crosslinked products, and on the stress-strain behaviors of the grafted products. The degree of grafting was found to be dependent mainly on the initiator and monomer concentrations. Increasing the initiator concentration increased the degree of grafting, and at the same time, increased the amount of gel (crosslinking). An increase in gel content of the grafted products resulted in a change of tensile behaviors from uniform deformation followed by strain-hardening at high strains to low extensibility and fracture at low strains.