Experimentally and theoretically analyzed processes occurring in mixtures of powders Ti-Al-Fe-Fe2O3 during reactive sintering (sintering from chemically interacting components) under controlled heating. As one of the components wastes of steel billets were used. This makes the study relevant. The heating rate was varied. Possible physical and chemical stages, their sequence and the assumed phase composition of the synthesis products were analyzed. Although reactive sintering has attracted considerable interest for the production of composite materials, the regularities established for binary systems cannot be purely transferred to sintering powders of more than two kinds. It is shown that the multistage process results in the formation of sets of nonequilibrium phases of variable composition based on α-titanium solid solution. The structures obtained from powder compositions «Ti+Al+Fe» and «Ti+Al+metal chips» do not differ much from each other, despite the presence of an appreciable share of oxides in the latter. The examples of particular problem solutions which correspond to the possible variants of diffusion interaction in a heterogeneous system are presented. Analytical solutions are obtained in the quasi-stationary approximation. The diffusive nature of changes in the position of interfaces is the same for constant and variable diffusion coefficients. The shape of the refractory reagent particle has little effect on the dynamics of the process. An example of calculating the stresses and strains in a conditional reaction cell when the phases are separated by moving boundaries is given. In the quasi-static approximation, the time for the mechanical part of the problem is a parameter. It is shown that the driving forces of diffusion transfer may be related to local stresses, which, in turn, may be related to changes in composition.