The continuous growth of the plastic industry leads to a steady optimization of technical production processes. Supported by the development of the computer technology, modelling and simulation tools provide the possibility to reproduce and analyze complex processes like plastics processing using co-kneaders. A co-kneader is an extruder with the particularity of an axially oscillating screw. Therefore, the rotatory movement of the screw gets superposed by an axial screw movement. In combination with kneading pins within the cylinder, the co-kneader ensures an efficient plastics processing. The present work deals with three-dimensional numerical simulation of a co-kneader in the open source software OpenFOAM. Starting from the real process, the simulation model is successively simplified on the basis of suitable assumptions. Using a simplified stationary Newtonian simulation model, various geometry and process parameters are finally investigated. The present work thus provides initial insights into the flow processes in the co-kneader.