The work aims to calculate and analyze structural stability and elastic properties of two kinds of iron nitrides, ζ-Fe2N and ε-Fe3N. First principles were adopted to simulate calculation method. The theoretical lattice constants of two phases coincided with well with the experimental ones, and the formation energy of two phases was negative. Corresponding polycrystal elastic properties were acquired based on monocrystal elastic constants of two phases. The calculated bulk modulus (B), shear modulus (G) and Young’s modulus (E) were all higher than the experimental ones. There was a certain proportional relationship between calculated and experimental values of ε-Fe3N polycrystal elastic property approximately at 1.3∶1, which was applicable to bulk modulus of γ‘-Fe4N. The B/G ratio of ζ-Fe2N and ε-Fe3N was 2.63 and 2.16 respectively. ζ-Fe2N and ε-Fe3N are provided with certain degree of thermodynamic stability. The shear modulus and Young’s modulus of two phases are close to or superior to those of steel, and the B/G values indicate their ductile nature. The elastic anisotropy of two nitrides is closely related to their crystal structures.