Numerical simulation of changes in the structure of cement composites performed for a wide range of varying factors makes it possible to develop optimal technological modes for producing concrete with desired characteristics. The complexity of physical and chemical processes, by which concrete gains strength, contributes to the development of various model approaches, each of which has a number of limitations. In this paper, the model of coupled processes in reacting media is modified to describe the structural changes of cement stone in the presence of fine polyfractional inert aggregate in the early stages of strength gain (hydration). It is believed that the initial blend after mixing with water has a macroscopic structure. The maximum achievable packing density of fine inert filler helps to improve the mechanical and microstructural characteristics of concrete and is ensured, in turn, by the optimal choice of the proportions of individual fractions in the entire volume of filler (sand). The material throughout the considered volume is assumed to be a heterogeneous medium that is based on both reactive components and inert substances of different concentrations, including pores. The possibility of forming a substructure of contacting particles of inert filler at various hierarchical levels is taken into account. The characteristics of cement are set in accordance with the mass fractions of clinker minerals that contribute to the hydration activity of the binder. Thermal processes are described by two temperature heat balance equations, which are solved by the finite difference method using the central difference scheme. At a time of heating the volume of the mixture caused by the exothermicity of a hydration reaction, the problems of macrokinetics and filtration are solved. Macrokinetic transformations are found in terms of the activation energy determined by isothermal calorimetry during cement setting at temperatures of 20, 30 and 40°С. Forced filtration of the liquid phase is assessed taking into account the capillary pressure caused by the peculiarities of the pore structure formation of cement stone.