The paper considers a theoretical model for the study of the process of transfer of sulfate ions in saturated porous media - mineral composites. In its turn, the model treats diffusion of sulfate ions into cement based composites, accounting for simultaneous effects such as filling of micro-capillaries with ions and chemical products and liquid push out of them. The proposed numerical algorithm enables one to account for those simultaneous effects, as well as to model the diffusive behavior of separate sections of the considered volume, such as inert fillers. The cases studied illustrate the capabilities of the proposed model and those of the algorithm developed to study diffusion, considering the specimen complex configuration. Computations show that the theoretical assumptions enable one to qualitatively estimate the experimental evidence and the capabilities of the studied composite. The results found can be used to both assess the sulfate corrosion in saturated systems and predict and estimate damage of structures built of cement-based mineral composites.