The paper analyzes the reaction of phase formation occurring during the synthesis in the Al-TiO2 system. The problem of the phase composition change in the vicinity of the particles, where the change of the regions occupied by the phases is related to the moving boundaries, is formulated. An approximate analytical solution is constructed. Kinetic regularities of the strengthening particle formation and the matrix composition evolution in its vicinity have been studied under the assumption that the reactions start at a temperature higher than the melting temperature of aluminum, which surrounds the titanium oxide solid particles. The temperature is a function of the time and follows from the solution of the macro problem. The accompanying stresses and strains both in the vicinity of the interface and averaged over the cell volume are evaluated. During cooling both diffusion and reactions are inhibited, which leads to slowing down the growth of stresses, however, their values remain rather high.