Measurements of neutron elastic and inelastic scattering from 56Fe have been analyzed theoretically. The shape-elastic-scattering cross sections, calculated with an optical-model potential using energy-independent parameters, added to the compound-elastic contribution obtained from a Hauser-Feshbach calculation, including width fluctuation corrections, agree reasonably well with the data from 4 to 7.6 MeV. Inelastic-scattering cross sections from the Hauser-Feshbach calculation agree well with the data from 1 to 7.6 MeV. From the known branching ratios for the decay of the levels of 56Fe, calculated gamma-ray-production cross sections are in reasonable agreement with the data. It is suggested that such calculations form the basis for consistent sets of (n,n′) and (n,n′γ) cross sections for shielding calculations.