Mechanical moduli, such as Young’s modulus (E), Bulks modulus (B), Shear modulus (S), longitudinal modulus (L), Poisson’s ratio (σ) and micro Hardness (H) were theoretically calculated for (100-x)TeO2+x MgO glasses, where x = 10, 20, 30, 40 and 45 mol%, based on the Makishima–Mackenzie model. The estimated results showed that the mechanical moduli and the microhardness of the glasses were improved with the increase of the MgO contents in the TM glasses, while Poisson’s ratio decreased with the increase in MgO content. Moreover, the radiation shielding capacity was evaluated for the studied TM glasses. Thus, the linear attenuation coefficient (LAC), mass attenuation coefficient (MAC), transmission factor (TF) and half-value thickness (Δ0.5) were simulated for gamma photon energies between 0.344 and 1.406 MeV. The simulated results showed that glass TM10 with 10 mol % MgO possess the highest LAC and varied in the range between 0.259 and 0.711 cm−1, while TM45 glass with 45 mol % MgO possess the lowest LAC and vary in the range between 0.223 and 0.587 cm−1 at gamma photon energies between 0.344 and 1.406 MeV. Furthermore, the BXCOM program was applied to calculate the effective atomic number (Zeff), equivalent atomic number (Zeq) and buildup factors (EBF and EABF) of the glasses. The effective removal cross-section for the fast neutrons (ERCSFN, ∑R) was also calculated theoretically. The received data depicts that the lowest ∑R was achieved for TM10 glasses, where ∑R = 0.0193 cm2 g−1, while TM45 possesses the highest ERCSFN where ∑R = 0.0215 cm2 g−1.