A new method of calculating steady-state neutron distributions in moderator materials is developed using the method of stochastic processes. In this method neutron life histories are considered as stationary Markoffian time series. The probability distribution for the neutron to be in a particular point in phase space as a function of time from neutron birth is then found by solving an appropriate Fokker-Planck equation whose coefficients depend on the one-collision probability distributions. This method has important applications to calculations of flux spectra and to shielding problems involving deep neutron penetration. When simplifying approximations are made, solutions for the flux have the correct qualitative features of the Boltzmann equation solutions. Quite good quantitative agreement is obtained with the Bethe-Tonks-Hurwitz solution of the Boltzmann equation. Effects of absorption, anisotropic scattering, and a mixture of materials can also be included. By the present method the neutron flux distribution can be calculated in position, lethargy, velocity angle, and possibly other variables, for a homogeneous infinite moderating medium at both large and small distances from the source. The neutron flux spectrum from an infinite plane source in an infinite medium has been calculated, as well as the angular distribution of the neutrons. Constant cross sections and high atomic weight are assumed but it is pointed out that these restrictions can both be relaxed.