Gamma-ray exposure buildup factors are calculated using a discrete ordinates direct integration code, PALLAS-PL, SP-Br, for water, concrete, iron, and lead, typifying materials of low, medium, and high atomic number. The radiation sources considered were both plane, at normal incidence, and at plane-isotropic. These data include the effects of secondary photon sources arising from Compton scattering, bremsstrahlung, and annihilation. Inclusion of a bremsstrahlung source influences the exposure buildup factors for high-energy photons in materials of high atomic number. The calculational accuracy is verified by comparing the PALLAS calculations with the results of experiments with both the energy spectrum and the attenuation dose transmitted through lead where the source is a plane isotropically incident 6.2-MeV gamma ray or a plane normally incident ∼8-MeV gamma ray. Comparisons are also made with other calculations of exposure buildup factors in water for a 0.5- and a 3.0-MeV plane normally incident source. The calculated buildup factors in each material are tabulated for incident energies of 0.1 to 15 MeV (except for lead where the lower energy is 0.4 MeV) and for penetration depths as great as 40 mfp.