Slant-path photon buildup factors for nine radiation shielding materials (air, aluminum, concrete, iron, lead, leaded glass, polyethylene, stainless steel, and water) are calculated with the most recent cross-section data available using Monte Carlo and discrete ordinates methods. Discrete ordinates calculations use a 244-group energy structure based on previous research at Los Alamos National Laboratory (LANL) and focus on the effects of group widths in multigroup calculations for low-energy photons. Buildup-factor calculations in discrete ordinates benefit from coupled photon/electron cross sections to account for secondary photon effects. Also, ambient dose equivalent buildup factors were analyzed at lower energies where corresponding response functions do not exist in the literature. The results of these studies are directly applicable to radiation safety at LANL, where the dose-modeling code PANDEMONIUM is used to estimate worker dose in plutonium-handling facilities. Buildup factors determined in this work will be used to enhance the code's modeling capabilities but also should be of general interest to the radiation shielding community.