The system and method is for the pumping of finely divided cellulose material to a continuous digester. The system has a concentric arrangement of pipes. A fluid (Liq) is added to a chamber formed between the pipes to establish a cylindrical film of fluid around a rod-shaped flow of cellulose material before the inlet to the pump. It is possible in this way to reduce the pressure drop in the lines, reduce wear in the pump, and ensure a maximal pressure build up in the pump.