Abstract A numerical study of cold neutron production in cryogenic moderators composed of solid or liquid CH 4 at temperatures ranging from 20.4 to 111.7 K is made. The study is performed by a multigroup neutron transport analysis with a set of energy-averaged cross-sections (group constants) generated by the authors. Particular attention is paid to the total and angular properties of a space–energy cold-neutron flux, especially in terms of an equilibrium energy spectrum at each temperature, a storage property of high-density cold neutrons and an anisotropic emission of cold neutrons from the moderator surface.