Nanostructured CrN hard coatings deposited by PVD are widely used in forming tools, cutting tools and casting moulds. The coatings are often under compressive residual stresses in order of several GPa induced by the coating process. If coating-substrate compounds are exposed to temperatures exceeding the deposition temperature, a reduction of compressive residual stresses by mechanisms like migration and annihilation of point defects, rearrangement and annihilation of dislocations, growth and coalescence of grains, recrystallisation and creep takes place. In this diploma thesis a material model is developed that describes the reduction of compressive stresses by a shrinking of the coating depending on current in plane stress in the coating and temperature. For calibration of the material model isothermal relaxation tests were used. The material model was implemented in the FEM program ABAQUS, in order to simulate a relaxation test under nonisothermal conditions and cyclic thermal shock experiments imitating loading conditions similar to those occurring at cutting edges. A comparison of calculated and experimentally measured residual stresses shows that there is a very good accordance in case of the nonisothermal relaxation test. Even under complex loading conditions occurring in the cyclic thermal shock experiments the behavior of the coating is reproduced well by the material model.