Abstract The three independent single-crystal elastic-stiffness constants C ij of cubic γ′-Fe 4N (face-centred cubic (fcc)-type iron substructure) have been calculated by first-principles methods using the density functional theory: C 11 = 307.2 GPa, C 12 = 134.1 GPa and C 44 = 46.0 GPa. The Zener elastic-anisotropy ratio, A = 2 C 44/( C 11 − C 12) = 0.53, is strikingly less than 1, implying 〈1 0 0〉 as stiffest directions, whereas all fcc metals show A > 1. This elastic anisotropy is ascribed to the ordered distribution of N on the octahedral interstitial sites. X-ray diffraction lattice-strain measurements for a set of different h k l reflections recorded from γ′-Fe 4N 1− y layers on top of α-Fe confirmed the “abnormal” elastic anisotropy of γ′-Fe 4N 1− y . Stress evaluation, yielding a compressive stress of about −670 MPa parallel to the surface, was performed on the basis of effective X-ray elastic constants determined from the calculated single-crystal elastic constants C ij and allowing a grain interaction intermediate between the Reuss and the Voigt models.