The numerical simulation of the tension levelling process by use of commercial Finite Element (FEM) software packages is reliable but yields unacceptable computational costs. A novel 2-D plane strain model of this process presented in this paper combines the advantages of a problem-specific ?Arbitrary Lagrangian-Eulerian? (ALE) formulation and a novel parameterization concept based on ?Parametric Shape Functions? (PSF) for the geometry and strain state of the deformed strip. Compared to (already optimized) models based on Lagrangian FEM-concepts, the number of degrees of freedom (and, hence, the computational costs) could be reduced drastically. The tailor-made PSF model was elaborately tested and validated using measurement data from an industrial tension leveller. The model allows for a deeper understanding of the tension levelling process: In extensive parametric studies, the plastification behaviour of the strip, as well as the optimization of the process-roll adjustments, were analyzed thoroughly. Selected key results of these investigations are presented in this paper.