A 3D model for heat transfer and stress evaluation during plasma spraying was developed for MSC/MARC. The substrate-layer system is represented by a sheet metal (strip) with the dimensions 120x20x2 mm and a zirconium dioxide+7% yttrium oxide layer with a thickness of 0.06 mm. In this paper, the following stages of the plasma spray coating process are simulated: coating application and natural cooling of the substrate-layer system. A transition problem of the heat transport and stress-deformation state of the three-dimensional substrate-layer system is solved by considering the stress relaxation through plastic deformation and crack formation (flaking). The results from three different models are discussed: an elastic model, a model with stress relaxation due to plastic deformation, and a model with plastic deformation and cracking. Paper includes a German-language abstract.