The linear attenuation coefficients of water and some solid phantom materials, namely of solid water RMI-457, of plastic water, of RW3 solid water, and of Perspex were determined by Monte Carlo calculations, for gamma-ray photons with energies of 59.5, 80.9, 140.5, 356.5, 661.6, 1173.2, and 1332.5 keV. The calculated values were compared with the experimental results presented by other researchers and with theoretical values obtained using the XCOM database. Good agreement was observed between the calculations, the experimental, and the theoretical values. The results indicate that the process in Monte Carlo code can be followed to determine the equivalency of other materials at several energies. Three shielding factors such as half-value layer, tenth-value layer, and mean free path were calculated at all considered gamma-ray energies.