Abstract. This paper demonstrates the influence of several approximations of FGM thermal barrier coatings on the temperature and stress distributions. It is shown that the conventional approximations by specific power or exponential functions reflect FGM distributions coming from neither theory nor practise. As example, a thick-walled cylinder including FGM TBC subjected thermo-mechanical loading is considered. Two independent formulations of the uncoupled thermo-elastic problem based on the displacement or stress function are tested.