The relations established until now for the pressure variation along a Maddock or Egan barrier type mixing device come from the extrusion theory developed for the metering zone; one used the same essential boundary condition, namely the barrel is rotated, while the screw is stationary. Here a different way to solve the problem is proposed, i. e. rotating screw and a stationary barrel. A new theory is developed by considering Poisseuille and drag flow through the channels, couette and drag flow through the clearance over the barrier flight. Relations are established for pressure variation along each channel, as well as in the barrier clearance. On this basis calculates the total pressure variation between inlet and outlet of the mixing section. The theoretical results are applied to a practical case and they are close to experimental results reported in the literature.