A reasonable physical model for the slowing down of gamma rays in infinite media is presented, and a method of numerical solution is described. Equilibrium energy spectra due to a fission source of gamma rays are shown for water, aluminum, iron, zirconium, and lead. In addition, energy spectra in aluminum, iron, and lead, due to the corresponding (n, γ) source in each metal, are presented. The use of infinite medium calculations to obtain a lower energy cutoff for a gamma heating problem is suggested. It is shown that for the case of a fission source, essentially all of the source energy is absorbed above 0.05 MeV in the materials studied, except in the case of water where approximately three percent of the energy is absorbed below 0.05 MeV. The infinite medium spectra are used to average absorption and slowing down cross sections for fuel materials and metals, and the resulting group constants are compared with similar calculations using a fission-source spectrum as a weighting function. Large differences are noted in many instances. Calculations of spatial energy deposition in simple model problems indicate that such differences in group constants can lead to local errors of significant magnitude.