The stability of coating-substrate-systems in uences the chip formation and the surface integrity of the new generated workpiece surface, too. Using FE simulation, deformations, strains and stresses in coated tools, caused by external and internal loads, can be computed on a microscopic scale. Since both, the whole macroscopic tool (in mm-scale) and the microscopic coating layers (in m-scale up to nm-scale) must be included in the same geometrical simulation model, graded high-resolution FE meshes must be used. Nevertheless, the number of nodes in the 3-D computational FE grid reaches some millions, leading to large computational time and storage requirements. For this reason, an Advanced Adaptive Finite Element (AAFEM) software has been developed and used for the simulation.