The stress state in thermal barrier coating systems is studied using the finite element method. It is shown that creep properties of the thermally grown oxide (TGO) layer strongly influence the resulting stress state. If the TGO is purely elastic, very large tensile stresses will occur due to the volume increase during TGO growth, allowing the propagation of cracks through the structure. If TGO creep is sufficiently rapid, these stresses are completely relaxed at high temperatures. In this case, failure is caused by the mismatch in the thermal expansion coefficients of. the materials. It is shown that even in the case of complete stress relaxation at elevated temperatures, a TGO layer of several micrometer thickness will cause large cooling stresses in the thermal barrier coating that allow the coalescence of microcracks.