Has been developed the mathematical model for the process of polymerization of ethylene under high pressure. This process is going on under non-stationary conditions, which is caused by the presence of acetylene formed during ethane pyrolysis. Acetylene is a poison for the initiator leading to decrease quality and productivity of polyethylene. For maintaining productivity at a constant level has been proposed a function that takes into account the poisoning effect of acetylene on it. Entering it into the mathematical model of the process will allow us to stabilize the process at any time of the reactor.