The aim of the present work is to introduce a thermodynamic model to describe the growth of an oxide layer on a metallic substrate. More precisely, this paper offers a study of oxygen dissolution into a solid, and its consequences on the apparition of mechanical stresses. They strongly influence the oxidation processes and may be, in some materials, responsible for cracking. To realize this study, mechanical considerations are introduced into the classical diffusion laws. Simulations were made for the particular case of uranium dioxide, which undergoes the chemical fragmentation. According to our simulations, the hypothesis of a compression stress field into the oxidised UO2 compound near the internal interface is consistent with the interpretation of the mechanisms of oxidation observed experimentally.