Abstract: In a process for preparing homo- or co-polymer of ethylene, in which ethylene alone or mixed with one or more other unsaturated organic compounds capable of forming a copolymer with ethylene is subjected to a high pressure and a high temperature in a reactor in the presence of an initiator or a catalyst, in which the mixture of polymer and unconverted monomer discharged out of the reactor is expanded to, practically, atmospheric pressure with the aid of an expansion device in two or more steps, and in which the polymer present in the expanded mixture is separated from the mixture in the solid state, the improvement which comprises obtaining the polymer in a fibrous form by supplying the mixture to the last stage of the expansion device at such a pressure and temperature that, during the expansion, in this last stage, the polymer passes from the liquid phase to the solid phase.