Shielding characteristics of iron, lead, ordinary concrete, heavy concrete, graphite, marble, water, and paraffin were calculated for monoenergetic source neutrons with energies <400MeV. The depth dependence of neutron and secondary photon transmitted dose equivalents at the exit surfaces of shields of varying thickness is exhibited for some monoenergetic source neutrons and for each material. Their shielding characteristics are compared and discussed in terms of the degradation process of neutron energy and the change of neutron spectrum in typical shielding materials. Calculations were carried out by using the one-dimensional discrete ordinates code ANISN-JR and the cross-section library DLC-87/HILO. Systematic knowledge concerning the shielding of neutrons with energies <400 MeV was successfully obtained.