This paper presents a non-linear infinite dimensional bi-zone model of an extrusion process through the representation of two systems of conservation laws coupled by a moving interface. The interconnection is performed under the assumption of constant viscosity along the extruder. In order to illustrate the behaviour of the model, the finite volume method is extended by using a color function to deal with a moving interface. Some simulations with variable screw speed are presented in order to illustrate the behaviour of the proposed model.