Gamma ray build-up factors of concrete shielding have been investigated by Geometrical Progression fitting formula for photon energy range 0.01-15 MeV up to 40 mfp penetration depth. The energy absorption build-up factors and Exposure Build-Up Factor (EBF) of concrete shielding have been studied as a function of photon energy, penetration depth, concrete density and chemical element compositions. The EBF of the concrete shielding having high equivalent atomic number increases rapidly beyond 3 MeV photon energy for high penetration depths. The build-up factors show that the heavy concretes (≥ 3.5 g cm−3) are good biological shielding. Steel-magnetite (5.11 g cm−3) is the best shielding concrete for reactor core for power operation as well as accidents. Present build-up factors are very useful for selection of shielding materials for reactor core in controlling the gamma exposure to the people involved and the public of photon energy abundance in the range of 0.1010 MeV.