In this work, the radiation shielding properties of 40Na$_2$O–(60–x)P$_2$O$_5$–xGeO$_2$ and 40Na$_2$O–10B$_2$O$_3$– (50–x)P$_2$O$_5$–xGeO$_2$ glass systems, x = 0–30 mol%, were investigated for use in radiation protection applications. As a result, the mass attenuation coefficient (MAC) for phosphate and borate phosphate glass samples was simulated using the MCNP5 code within photon energies of 0.02–20 MeV, and the simulated MAC values were compared to those obtained theoretically using the XCOM database. Based on the simulated ${\mu}_m$, linear attenuation coefficient (LAC), half-value layer (HVL), mean free path (MFP) and effective atomic number (Z$_{eff}$) were determined. It was found that the ${\mu}_m$ decreased with the increase of photon energy and increased with the increase of (mol%) fraction of GeO$_2$. Because of its greater values of MAC, LAC, and lower values of HVL and MFP, the NaPGe-30 glass with a 30 mol% concentration of GeO$_2$ is shown to have improved gamma-ray shielding performance. The neutron shielding effectiveness of the phosphate and borate-phosphate chosen glasses was also tested in this study. Using the PhyX/ZeXTRa database, the effective removal cross-section (cm$^{-1}$) was computed. Finally, it was discovered that the NaBPGe-20 glass with a B$_2$O$_3$ concentration of 10 mol% and a P$_2$O$_5$ concentration of 30 mol% has better neutron shielding properties than the other glass samples, due to having the highest effective removal cross-section.