The aim of the present investigation is the development of a practical model for a high-pressure polyethylene plant. The reactor considered in the present work is an adiabatic slim type autoclave with four zones for free radical polymerization of low density polyethylene (LDPE). A fairly comprehensive, but realistic model is described that has the ability to predict the temperature at each reaction zone, as well as the effects of initiator flow changes. From stability analysis we can identify the range of operating conditions which can effectively be used to prevent runaway reactions, and maximize polymer conversion in LDPE autoclaves.