The mechanism of interaction between fast neutrons and atoms of a metal lattice is described. A cross section for the production of vacancies in iron by neutrons, as a function of neutron energy, is derived and shown to be roughly proportional to the product of the neutron energy and the isotropic elastic scattering cross section. The vacancy production cross section is applied to several reactor spectra and the results show that an appreciable fraction of the radiation damage in crystalline solids, particularly metals, can be caused by neutrons having energies below 1 Mev. Also the assumption that the neutrons responsible for radiation damage have a fission spectrum distribution appears to be inapplicable in reactor situations. In fact, no quantitative measure of total neutron exposure can be made without knowledge of the spectral shape. Steel is chosen as an example because of the interest in its properties as a function of irradiation, hence the model is developed based on interaction of neutrons with iron atoms. Some important limitations of the method are cited.