Abstract: Neutron-induced irradiation damage is a major challenge for nuclear energy systems. Neutron irradiation damage is initiated by neutron-induced nuclear reactions and often quantified by the displacement damage, of which the conventional unit is the number of Displacements per Atom(DPA). Displacement damage is a consequence of atomic collision cascades in materials induced by recoil nuclei, which are referred to Primary Knock-on Atoms(PKAs) in radiation damage. Therefore, nuclear reaction data or nuclear reaction models are required to evaluate the neutron-induced displacement damage. Due to the lack of complete recoil spectra in the current evaluated nuclear data files, the calculation of displacement damage cross section (and thus the subsequent evaluation of irradiation damage level) should be based on the available differential cross sections and conservation laws. After the presentation of the two paths for evaluating neutron-induced displacement damage, the present work thoroughly summarizes the methods for computing displacement damage cross sections induced by different nuclear reaction types, including discrete and continuum binary reactions, neutron capture reaction, and the detailed discussion on many-body reactions. Then, the DPA cross sections of potential accident tolerant cladding material FeCrAl are calculated for various Cr and Al contents based on the recently evaluated ENDF/B-VIII.0 nuclear data library. Preliminary results show that the evaluation of neutron irradiation-induced DPA for FeCrAl is not sensitive to the content of Cr and Al, whereas the DPA in FeCrAl should be about 3%~4% higher than that in pure iron. The former conclusion implies that the evaluation of neutron irradiation-induced displacement damage can be performed with “arbitrary” contents of Cr and Al. However, it should be noted that the content of Cr and Al may influence the threshold displacement energies or the damage energy.