Studies on rheology and extrusion of wood-polymer composites WPC are very limited. Computer models currently available do not allow to simulate WPC extrusion correctly. Extensive experimental studies have been performed for single screw extrusion of PP/wood flour composites of WF concentrations (from 25% to 70%). Screw Pulling-out Technique was used to study material melting, screw filling, and pressure was measured. An effect of screw speed and flow rate (starvation level) was studied. It was concluded that WPC extrusion is totally different from extrusion of thermoplastics. Material transport and melting are strongly dependent on the composition and operating conditions. Contiguous solid melting mechanism CSM which is typical for flood fed single screw extrusion of thermoplastics was not observed for high content of WF. In this case, one-dimensional melting mechanism was seen, and melting occured at the solid bed/melt film interface, and the molten material penetrated the solid bed such that a melt pool was not formed at the active flight of the screw. With an increase of PP content, more than 50%, CSM mechanism appeared, and a melt pool at the active flight was formed which increased in width when melting progressed. WPC single screw extrusion has been simulated using GSEM program. This is a global model which includes solid conveying, melting and melt flow. The model allows to predict pressure and temperature profiles, melting of the polymer, etc. A new, one-dimensional melting model has been developed and implemented into the program code. Three-dimensional, non-Newtonian FEM simulations using Ansys-Polyflow have been performed for material flow with yield stress and slipping at the walls. Dimensionless screw pumping characteristics (flow rate vs. pressure gradient) have been developed and implemented into the program code to model the material flow in the extruder. FEM modeling for material melting has been discussed. Simulations have been validated experimentally. Acknowledgments: The authors would like to acknowledge support from National Science Center, Poland (DEC-2015/19/B/ST8/00948).