Experiments in which a wide range of scattering materials in the form of slabs were bombarded by reactor neutrons showed that the angular distribution of low-energy (<5-eV) neutrons leaking from the opposite side of a slab is independent of the source term and of the slab thickness for thicknesses greater than some minimum thickness zmin. In the case of pure lead, pure water, and mildly poisoned water, the resulting distributions are in agreement with the Fermi expression. The results for pure lead are also in excellent agreement with one-velocity calculations. An imperfect experiment with poisoned lead is in qualitative agreement with one-velocity calculations. The angular distribution for LiH is described byΦ(µ) = 1 +AµwhereAis less thanfor subcadmium neutrons and greater thanat 1.5 and 5 eV. For energies above 5 eV, a Monte Carlo calculation on LiH showed that A continues to rise to a peak value of about 2.5 at 30 eV, after which it decreases to a value ofabove 103eV, where the absorption cross section of lithium becomes negligible. The applicability of two neutron transport codes that numerically integrate the Boltzmann transport equation was tested in additional calculations for LiH and water. Although the two codes have been used successfully in other types of shielding calculations, they yielded angular distributions for the same material that disagreed with each other, as well as with some experimental data. This suggests that the development of neutron transport codes should include angular distribution tests.