In this work, a distributed parameter bi-zone dynamic model with moving interface of an extrusion process is presented. In this case, a variable viscosity is assumed along the extruder. A finite volume method is proposed for discretizing the dynamic model. The steady-state values of the variables were calculated by using an efficient optimization algorithm. Experimental tests performed with an industrial type twin screw extruder are compared against simulations for the case of variable screw speed and constant feed rate. The comparison shows good qualitative agreement between experimental and simulation results. This model can be used to design observers for estimating non-measurable variables as well as advanced control strategies.