Using the full-potential-full-electron-linearized-augmented-plane-wave (FLAPW) method, we carried out ab initio calculations of the electronic structure for austenitic steels of different compositions. The total set allows to find a system of equations for obtaining the value and sign of the interatomic bond energy between Fe-Fe, Fe-Mn, Fe-Cr, Fe-Ni; Ni-Ni; Cr-Cr, Mn-Mn and Mn-Cr. It is obtained that both Cr-Cr and Cr-Fe bonds are attractive, however the Cr-Cr bonds are stronger. The interaction between interstitial carbon (nitrogen) and metallic atoms is calculated. The interstitial atoms change the metal-metal interaction between the nearest neighbors.