The moments method is applied to the problem of calculating neutron distributions in an infinite medium. Several comparisons are given of these results with similar data calculated by the discrete ordinates method. New calculations are presented on the distribution of doses from neutrons, originating in a plane-slant fission source and incident, at various angles, on concrete utilized in radiation measurements at the Tower Shielding Facility of the Oak Ridge National Laboratory (TSF concrete). For a given set of neutron cross sections, these results give reliable estimates of the dose distribution at deep penetrations, i.e., attenuation of six orders of magnitude or more. Functional representations of the distributions are included in order to facilitate the use of the data in shield design calculations.