A general model is developed for numerical calculations of neutron slowing down parameters and functions in homogeneous media of any composition. The model is based on a representation of slowing down as a discrete time, discrete state Markov process. It is shown that the weighting function normally used in calculating elements of a multigroup stepping array is not optimal for discrete calculations. An improved weighting function is developed and used to define a model for Markovian transition probabilities. The relation defining Markov n-step transition matrices is utilized to generate stepping matrices that are consistent, accurate, and stable regardless of energy range or time step width. This relation is also used to develop a calculational technique in which a stepping matrix follows the neutron pulse downward in energy, greatly extending the energy range and number of states or groups that may be used in a single calculation. The model is evaluated by comparing the solutions it produces to certain exact solutions of the slowing down equation. It is, in turn, used to evaluate some asymptotic and approximate analytical solutions of the slowing down equation and to explore some problems in slowing down theory.