The fabrication of TePbMgX glass system has been done using the standard melt quenching method. The number of bonds per unit volume (nb) increases from 7.77 x 10(22 )cm(-3) to 8.02 x 10(22) cm(-3). The values of E, K, G and L moduli decreases from 31.58 to 23.22 GPa for E, 14.79 to 11.76 GPa for K, 14.82 to 10.63 GPa for G and 34.55 to 25.93 GPa for L respectively as the PbO increases from 35 to 55%. The sigma lies in the range of 0.145-0.172. The indirect and direct band gap energies decrease from 2.832 to 2.673 eV and 3.120-3.005 eV respectively with increasing mol% of the PbO. Moreover, with the help of FLUKA code, we reported the mass attenuation coefficient (mu/rho) for the prepared samples between 0.122 and 1.458 MeV. The FLUKA results were compared with those generated from Phy-X software and a good agreement was reported and this validated the simulated mu/rho results. The linear attenuation coefficient (LAC) was determined to examine the influence of adding PbO on the shielding performance of the prepared samples. The LAC result suggested that the attenuation performance for the TePbMgX glass systems is highly effective when exposed to low energy radiation, and, by contrast, the glasses become worse attenuators when exposed to high energy radiation. Also, the glass with 55 mol% of PbO (MgO free) has a higher LAC than the glasses with 35-50 mol% of PbO (5-20 mol% of MgO). The half value layer (HVL) of the glasses greatly increase with increasing energy. For TePbMg1, the HVL increases from 0.050 cm at 0.122 MeV, to 1.559 cm at 0.779 MeV, and 2.573 cm at 1.458 MeV. This HVL results demonstrated that increasing the PbO content in the glasses improves the shielding ability of the glass system, with TePbMg5 having the best HVL at all energies. At 0.3443 MeV, the effective atomic number (Z(eff)) values increase from 48.40 for 35 mol% PbO, to 49.87 for 40 mol% PbO, 51.28 for 45 mol% PbO, 52.62 for 50 mol% PbO, and 53.89 for 55 mol% PbO. We calculated the Relative reduction in transmission (RRT) and we found that at 0.245 MeV, the RTT values at 0.245 MeV have the following values: 17% and 81% for the samples with thickness of 0.25 and 2.25 cm respectively.