Co-rotating twin-screw extruders (TSE) are widely used in today’s polymer processing and food industry. In recent years, they attracted increasing interest in the pharmaceutical industry. Complex screw geometry, melt rheology, melting zone and partially filled sections make the simulations highly challenging. Conventional mesh-based CFD (Computational Fluid Dynamics) methods require sophisticated remeshing algorithms to account for the screw rotations. Partially filled sections cause additional challenges due to free surface flows. SPH is a mesh-free, Lagrangian method for the simulation of fluids by representing the flow field with small fluid elements. This allows SPH to inherently account for free surface flows and convective mixing, in contrast to CFD methods. To account for the complex geometry of extruder screws, a novel wall interaction method was developed, allowing the direct use of the wall geometry without additional particles. With that, the Newtonian flow in a conveying element was analyzed with the open-source particle simulator LIGGGHTS. The results were compared to CFD data from the literature, which showed excellent agreement. Additionally, the flow in various screw elements was investigated for complete and partial filling. This yielded data for the conveying ability, pressure generation, power input and mixing of these screw elements in different operation states. In order to enable the simulation of the typically complex rheology of polymers, non-Newtonian viscosity models for SPH were implemented into LIGGGHTS. The implementation was validated with finite difference solutions for a pressure driven flow between two plates. Moreover, the thermal energy equation will be included in order to gain information about the local melt temperature, and to account for the temperature dependency of material properties. This will be used to study the non-Newtonian and non-isothermal flow in completely and partially filled screw elements.