Mathematical model of selective and competitive oxidation of multi-component non ideal alloys is used for modelling oxidation of Fe-Cr-Ni alloys. The model is based on: a) the Danielewski-Holly model of interdiffusion, b) the Wagner model of the Ni-Pt alloy oxidation, c) the postulate that the values of fluxes in reacting alloy are limited (the kinetic constraint) and d) the thermodynamics of the Fe-Ni-Cr system. In this paper for the first time modelling of oxidation of a ternary non-ideal alloy based on Danielewski-Holly model is presented. The model is used to predict the evolution of component distributions in the reacting ternary Fe-Cr-Ni alloy. The results of the modelling of oxidation of the 316L stainless steel at 1173 K are presented. We compute the chromium depletion during the long term oxidation. The results allows to conclude that the oxidation reaction is limited by interdiffusion in reacting alloy. The computations demonstrate that the chromium depletion is the key factor affecting the scale stability during the long time exposition.