An integrated global computer model MultiScrew System has been developed to model, optimize and scale-up polymer extrusion.At present, the system includes single screw screw extrusion model GSEM (flood fed and starve fed) and counter-rotating twin screw extrusion model TSEM. The particular models simulate an operation of the extruder-die system. Using the material and rheological properties of the polymer, the screw and die geometry, and the operating conditions, the models predict all the important process parameters (pressure and temperature profile, melting progress, flow rate, screw filling, power consumption etc.). The fundamental for models building are the experimental studies to develop the geometrical model of the process and to validate the solution. Studies on melting mechanism occuring in extrusion are of highest importance. The models are extended to advanced polymeric materials, i.e. polymer blends and composites (e.g. wood-plastic composites). A concept of FEM modeling of polymer melting in extrusion has been discussed. It involves modeling a two-phase flow (fluid/solid) as a single-phase flow, and melting progress is defined by temperature distribution which determines the regions of solid and fluid. Applying this approach, it is not necessary to know the melting mechanism. Evolution strategies (Genetic Algorihms) have been applied to optimize and scale-up extrusion process, where response surface is given by mathematical models of the process. Unlike other optimization approaches, Genetic Algorithms do not require any derivative data, are relatively fast and allow to avoid the local optima.