Gamma-rays and fast and thermal neutron attenuation features of (Bi 2 O 3 ) x –(TeO 2 ) (100− x ) (where x  = 5, 8, 10, 12, and 15 mol%) and (TeO 2 ) 0.7 –(B 2 O 3 ) 0.3 (1− x ) –(Bi 2 O 3 ) x (where x  = 0.05, 0.10, 0,15, 0.20, 0.25, and 0.3 mol%) glass systems have been explored and compared. For all samples, mass attenuation coefficients ( μ / ρ ) are estimated within 0.015–15 MeV photon energy range by MCNP5 simulation code and correlated with WinXCom results, which showed a satisfactory agreement between computed μ / ρ values by these both methods. Additionally, effective atomic number ( Z eff ), effective electron density ( N eff ), half-value layer (HVL), tenth-value layer (TVL), mean free path (MFP), total atomic cross-section ( σ a ), and total electronic cross-section ( σ e ) are calculated by utilizing μ / ρ values. The μ / ρ , Z eff , and N eff are energy dependent and have higher values at the lowest energy and smaller values at higher energies. Moreover, using the G–P fitting method as a function of penetration depth (up to 40 mfp) and incident photon energy (0.015–15 MeV range), exposure buildup factors (EBFs) and energy absorption buildup factors (EABFs) are evaluated. Both 85TeO 2 –15Bi 2 O 3 (mol%) and 49TeO 2 –21B 2 O 3 –30Bi 2 O 3 (mol%) samples, by possessing higher values of Z eff , exhibit minimum EBF and EABF values. Highest μ / ρ , Z eff values and lowest HVL, TVL, MFP values of 49TeO 2 –21B 2 O 3 –30Bi 2 O 3 (mol%) sample indicated its better gamma-ray absorption capability among all selected glasses. Further, macroscopic effective removal cross-section for fast neutrons (Σ R ), coherent scattering cross-section ( σ cs ), incoherent scattering cross-section ( σ ics ), absorption cross-section ( σ A ), and total cross-section ( σ T ) values for thermal neutron attenuation have been computed. Among all samples, 49TeO 2 –21B 2 O 3 –30Bi 2 O 3 (mol%) glass possesses a better Σ R value for fast neutron attenuation, while the largest ‘ σ T ’ value of 66.5TeO 2 –28.5B 2 O 3 –5Bi 2 O 3 (mol%) sample suggests its good thermal neutron absorption efficiency.