This Master thesis is the result of a cooperative project between the Chair of Mechanics at the University of Leoben and HOERBIGER Wien GmbH. The aim of this thesis is to investigate the mechanical behaviour of polymer-based packing rings in industrial reciprocating piston compressors by means of the finite element (FE) method. Polymers show some specific features in their mechanical behaviour, among others that they tend to creep already at room temperature. The FE model is generated automatically using a Python script. To validate the modelling assumptions of the FE model, the FE results are compared with the analytical solution from plate theory (Kirchhoff and Mindlin-Reissner) under the assumption of linear-elastic material behaviour. The comparison with the analytical solution shows that the deformations due to shear stress outweigh the deformations due to bending. The parameters of a viscoelastic/viscoplastic material model are calibrated from the material data provided by HOERBIGER Wien GmbH. The material model takes into account the time dependence of the mechanical material behaviour as well as the temperature and load dependence. Furthermore, the influence of the different system parameters (time, pressure difference, temperature, friction, and pressure gap width) on the creep behaviour of the packing ring is investigated. The influence of the geometry parameters is also studied. The results show that temperature, pressure difference and pressure gap width have the strongest impact on the creep behaviour. The results also show that the axial ring thickness is the only relevant geometrical parameter. Using the FE analysis and the calibrated material model, the behaviour of the packing ring is simulated over the operating time. With this simulation data, an interpolation function for the displacement depending on pressure and pressure gap width is proposed. Using this interpolation function and a defined deformation limit value, the permissible pressure gap widths are determined. With the help of automatically generated three-dimensional FE models, the influence of pressure balancing elements (pressure balancing holes) on the creep behaviour of the material is investigated. In a parameter study, the diameter and position of the pressure balancing holes are varied. Furthermore, the influence of asymmetry of the pressure gap on the creep behaviour of the material is investigated.