  In this paper we deal with the problem of predicting a steady-state neutron
spectrum in media of arbitrary composition and geometry. The analytical
calculations of such spectrum are often too complex, if at all possible. We
describe a method of Geant4-based Monte Carlo calculation of the steady-state
neutron spectrum in a medium containing a fixed neutron source. In addition to
the steady-state spectrum, we obtain the snapshots of the neutron spectrum
evolution in time, which may be thought of as the non-equilibrium neutron
spectra, and their form is of considerable interest for further studies.
