Thin coatings are widely applied to protection of cutting tools against corrosion and wear. First of all, it is refractory coatings on the basis of such compunds as TiC, TiN and TiAlN which many times over increase the work life of tools. However still there is no clear understanding of details of interaction of these coatings with material of a cutter, mechanisms of their influence on efficiency of the cutting process and on durability of the tool. This understanding can be reached fully only on the basis of quantum-mechanical modeling which allows to study physical and mechanical processes at the atomic level. One of the most important characteristics of any coatings is the adhesion energy that is the work for separation a coating from a substrate. In this article results of a quantum-mechanical study by methods of the density functional theory and the pseudo-potential, taking into account spin polarization, the adhesion durability of nanodimensional coatings of TiC, TiN and TiAlN on the surface of iron (the main component of steel) and cobalt (binding material of hard-alloy cutters like WC-Co) are described. Calculations have shown that the adhesion energy of these coatings on iron and cobalt is enough for ensuring their reliable coupling of these compounds with the cutting tool when cutting and lies in the range of 3,5-4,1 J/m that is coordinated with the available literary data. The main physicomechanical characteristic which is responsible for wear resistance of the “coating-substrate” system in the course of its use as a cutter can be considered the shear module. In this work the calculations modeling shear deformations were carried out and the following values of the shear module have been obtained: G (GPa): G (TiC-Fe)=63; G (TiN-Fe)=68; G (TiAlN-Fe)=120; G (TiC-Co)=52; G (TiN-Co)=57; G (TiAlN-Co)=115. Calculated values of the shear module for coatings of TiC, TiN and TiAlN on cobalt are slightly lower than the values obtained for the same coatings on iron. Apparently, it is connected with a fact that contribution in elastic properties of the “coating-substrate” system makes not only a covering, but also a substrate; and the iron shear module (82 GPa) is bigger than the cobalt shear module (75 GPa). Both on an iron substrate, and on cobalt the following ratios are carried out: G (TiAlN-Fe/Co)> G (TiN-F/Co)> G (TiC-Fe/Co).