A nature of the forces, which act between the concrete cement matrix and entrained mineral particles (ground additives, fine and coarse additives), has been considered. It has been shown that the adhesion between them is attributable to the forces of different nature. The strongest adhesion between the particles of the hydrated binding material and mineral additives occurs, when materials, which react with calcium hydrate of the pore fluid, are used. The latter includes glassy wollastonite, which is part of granulated blast furnace slag. Even at a temperature of 25 °C, an aggressive interaction between them is observed and firm chemical bonds occur. In such case, the dissociation energy of such bonds ranges from 400 to 500 kJ per bond. Between materials, such as crystalline wollastonite and the concrete cement matrix, there is an epitaxial coalescence of its basal surfaces and tobermorite calcium hydrosilicates formed by the interaction of the binder with water. A direct contact is required between the reacting surfaces for such interaction. This is implemented by virtue of the bond, which is attributable to contraction forces resulting from shrinkage strains of the hydrated particles in the concrete cement matrix. Internal strains of the cement that are attributable to contraction, shrinkage, and carbonization of hydrated compounds result in the cement sheath contracting around the aggregate grains and steel reinforcement. Internal strains of the cement stone can be calculated using the Lame equation. We have reviewed the role of the factors, which are most critical for contraction of the cement ring around coarse particles of the aggregate and for stress-strain properties of artificial conglomerates, which have different composition and purpose.