Patterned ground structures characterised by strong heterogeneities in surface and subsur- face properties are a common feature of permafrost landscapes in the Arctic. In this thesis, an existing permafrost model including conductive heat transfer and the phase change of water is extended to simulate the thermal dynamics of polygonal soil structures in an Arctic tundra wetland in Northern Siberia. A two-dimensional model formulation in cylindrical coordinates is implemented and coupled to a surface energy balance model. The model performance is assessed by a comparison with analytical solutions and field measurements of soil temperature and surface heat fluxes. The heat transfer in the soil is represented well with mean absolute deviations of up to 1 °C. The coupled simulations with surface energy balance calculation represent the soil temperatures with larger deviations that can be attributed to the description of the snow cover in the model. Lateral heat fluxes in the polygon only occur during limited periods and do not have a substantial impact on the thermal dynamics of the system. Simplified one-dimensional model descriptions based on averaged soil and surface parameters show a cold bias of up to 0.7 °C in the mean annual temperature of the permafrost compared with the detailed two-dimensional model. The thaw depth is simulated consistently by the models of different complexity .