As a result of the expansion in the different uses of gamma ray sources and as a result of the harmful effects of radiation exposure, scientific research remains in need of finding and developing materials used as radiation shields. In the present study, shielding parameters of Sn-20Bi (SB) and Sn-20Bi-0.4Cu (SBC) lead-free alloys solidified with and without the effect of a rotating magnetic field (RMF) have been studied. Gamma ray mass attenuation coefficient (μt=ρ) was measured experimentally for the studied alloys at photon energy of 356, 511, 662, 1173, 1274, and 1332 KeV. The experimental μt=ρ values were compared with the calculated values by using the WinXCom and MCNP5 programs for alloys solidified without RMF. Besides, WinXCom and MCNP5 were used to calculate μt=ρ for gamma ray photons of energy range of 10 3-102 MeV. The atomic and electronic cross sections (σa and σe) and hence the effective atomic number (Zeff) and effective electron density (Neff) were calculated. The mean free path (MFP) of photons was calculated and introduced to MCNP5 input file to calculate the gamma ray energy buildup factor (EBF). The results of μt=ρ are shown to be highly compatible between the theoretical WinXCom and simulated MCNP5 programs and with the experimental values. The results of the shielding parameters confirm that the alloys under study are good shielding materials against gamma rays.