In the reactive extrusion process for the free radical grafting of acid monomers onto polyethylene, monomer grafting and homopolymerization occur simultaneously and interact with each other. Using an incremental theory, mathematical models of conversions for monomer grafting and homopolymerization were separately constructed to predict the grafting degree, mass of homopolymer and grafting efficiency. Effects of the barrel temperature, initial monomer and initiator concentrations on grafting behaviors were investigated. The barrel temperature and initial monomer concentration were shown to be the main process parameters for controlling the grafting degree. The grafting degree and mass of homopolymer increased significantly with increasing barrel temperature and monomer concentration and increased marginally with increasing initiator concentration. No significant improvement in the grafting efficiency was observed. The predictions of the models are in good agreement with experimental data. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40990.