Within the framework of the lattice-statics method and of the method of static fluctuation waves, the energies of strain-induced interaction of interstitial—interstitial (i—i), interstitial—substitutional (i—s), and substitutional—substitutional (s—s) impurity-atoms’ pairs are calculated and analysed for f.c.c.-(Fe,Ni)—C-isomorphous solid solutions with account of discrete atomic structure of the host-crystal lattice. The lattice spacing, elasticity moduli and/or quasi-elastic force (Born—von Karman) parameters of the host-crystal lattice, and concentration coefficients of the dilatation of the solid-solution lattice due to the corresponding solute atoms are the input numerical experimental data used. Energy of this interaction prove to be nonmonotonically decreasing (‘quasi-oscillating’) and anisotropic function of the discrete interatomic radius-vector, and itself interaction is strong and long-range. In all f.c.c.-(Fe,Ni)-base solid solutions, there is strain-induced attraction in some co-ordination shells. Generally, the strain-induced interaction between impurity atoms in $\gamma$-Fe is weaker than in $\alpha$-Ni, but in some solid solutions, it may be of the same order. The verification of applicability of the model of strain-induced interaction between impurities for Fe—C austenite by means of calculation of thermodynamical C activity and the ‘short-range order’ parameters of C-atoms’ distribution revealed by the Mössbauer spectroscopy showed that it must be supplemented by the additional short-range ‘electrochemical’ repulsion inside the first co-ordination shell. In any case, the strain-induced interaction of impurity atoms must be taken into account for analysis of structure and properties of f.c.c.-(Fe,Ni)-base interstitial (substitutional) solid solutions.