A comprehensive study of gamma-ray exposure build-up factors (EBFs) of fly-ash brick materials has been carried out for photon energies of 0.015-15 MeV up to a penetration depth of 40 mfp (mean free path) by a geometrical progression (GP) fitting method. The EBF values of the fly-ash brick materials were found to be dependent upon the photon energy, penetration depth and chemical composition, and were found to be higher than the values for mud bricks and common bricks. Above a photon energy of 3 MeV for large penetration depths (>10 mfp), the EBF becomes directly proportional to Zeq. EBFs of fly-ashes were found to be less than or equal to those of concrete for low penetration depths (<10 mfp) for intermediate photon energies up to 1.5 MeV. The EBF values of fly-ash materials were found to be almost independent of Si concentration. The fast neutron removal cross sections of the fly-ash brick materials, mud bricks and common bricks were also calculated to understand their shielding effectiveness. The shielding effectiveness of the fly-ash materials against gamma-ray radiation was lower than that of common and mud bricks.