Thermal stresses in diamond coatings deposited onto cemented carbide substrates are calculated using the finite element method. The thermo-elastic stress fields for some coating-substrate geometries are presented. The results are compared with experimental data on the tribological behaviour of diamond coatings. Residual stresses can explain many of the observed patterns of coating wear and failure. A model for the abrasive wear of brittle coatings under large compressive biaxial stresses is described. These stresses prevent cracks initiated at the surface to propagate towards the interface and may promote crack paths parallel to the interface, thus causing the formation of a smooth coating surface. Once the smooth appearance is reached it will become extremely hard to initiate and propagate cracks into the coating and consequently the wear rate becomes very low. Thus, large compressive residual stresses increase the already high wear resistance of diamond coatings. When diamond coatings are deposited onto substrate edges, intense concentrations of normal and shear stresses may lead to coating failure by interfacial spalling. These stresses are lowered by increasing the ratio r/h, where r is the edge radius and h is the coating thickness.