Elastic fields, generating by precipitates, cracks, dislocations and other defects of the structure, influence the diffusion processes. It leads to the alteration of the phase transformation kinetic, segregation formation and changes of the alloy properties. However, understanding the effects of strain on diffusion in solids is now limited. One of the chief aims of our approach is to obtain the general equations for the diffusion fluxes under strain that give the possibility of using these equations at low temperatures, as in this case, the strain influence on the diffusion fluxes is manifested in maximal degree. Recently some important generalization of our approach was done and equations for the vacancy fluxes in cubic metals were obtained. Now we have made the next step in the development of approach: general equations for the fluxes in interstitial alloys are obtained for different kinds of jumps in bcc and fcc structures. We are going to discuss the main features of the theory of diffusion under stress, to compare the equations for the fluxes and to present results of theory applications that are obtained with the help of computer simulations.