The Smoothed Particle Hydrodynamics (SPH) method is used to determine the flow through a model screw extruder at low Reynolds number with an emphasis on resolving the flow in narrow gaps, which are known to produce high shear rates and generate large temperatures. Firstly we demonstrate the validity of the SPH methodology by comparison on simple flows with known analytic solutions. We find excellent agreement and this also allows us to estimate the SPH particle size that is required to obtain accurate solutions for these and more complex flows. SPH simulations on a model single screw extruder with a kneading element are then compared with FEM solutions. Once again excellent agreement is achieved. Finally we demonstrate the SPH method on a model twin screw extruder, which is shown to be robust and qualitatively valid. In general these results show that SPH will be an important computational tool to investigate flows in similar devices. Crown Copyright (C) 2018 Published by Elsevier Ltd. All rights reserved.