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Polishing as a step of the manufacturing process is not only used in the finishing of optical elements made out of glass. An increasing number of applications needs shiny or glossy surfaces. For these parts, the specified roughness has to be achieved by a final polishing step while keeping or improving the final shape. The goal of the presented research is to predict the material removal that occurs during the polishing process by a simulation based on finite element modelling (FEM). The presented finite element simulation model for PMMA is based on the material parameters for workpiece and polishing tool. Compared to previous research on aspherical elements made out of glass [1], the model allows the description of the process based on material parameters get out the data sheets. The data derived from the finite element modelling is compared with the polishing results on plastic materials (PMMA). Results of the polishing tests compared with the simulated values will be reported.