We consider a porous periodic medium saturated by a fluid that contains a dissolved chemical substance. It is assumed that the solid matrix undergoes a progressive homogeneous dissolution at the microscopic scale. Such a case corresponds, for example, to the slow degradation mechanism of the rock at the long term during the geological storage of the CO2. Many other examples of application concerning natural and industrial materials, can be found. The following phenomena are taken into account: -The water flow through the pores (the “H-problem”) -The solid deformation (the “M-problem”) -The transport of dissolved chemical substance (the “T-problem”) -The chemical dissolution of solid (the “C-problem”) By applying the method of homogenization of periodic structures, the macroscopic model of the system was developed. The model contains, in particular, a formulation of the chemical degradation of the microstructure of the medium. As a practical example, the case of a porous medium with a 3D microstructure was considered. The numerical computations of the chemo-mechanical coupling showed the decrease with time of all non-zero components of the macroscopic stiffness tensor.