The free radical copolymerization reactor of the ethylene and VA is operated under the conditions of high pressure and temperature. In this study, a two-compartment four-cell model is used to describe the behavior of the adiabatic autoclave reactor for the EVA bulk copolymerization reaction. The parameters for various reaction rate constants are determined by analyzing the free radical and ethylene decomposition reaction mechanisms and associated data adopted in many studies. The bifurcation diagrams are constructed to investigate systematically the effects of various operation parameters on the reactor performance, and the feasible operating regions are analyzed. The overall structure of the steady states of the reaction system is examined by organizing the bifurcation set by two-parameter continuation method. The strategy for the production rate increase is also proposed by elucidating the relationship between the reactor performance and the molecular weight.