The time required to slow neutrons down to various energies in a hydrogenous moderator is calculated by the Monte Carlo method. Exponential distributions are used for logarithmic energy loss and for distribution of free paths, and empirical cross section data are used to calculate the mean transit time between collisions at each energy. Kesults are presented in tabular form, and it is further shown that the distribution of slowing-down times at epithermal energies is well represented by a Pearson type III curve. Results of the calculation are compared with experimental results in an accompanying paper.