Polymers doped with heavy metal oxide are proposed to shield the radiation workers from hazardous gamma-rays and neutrons originating from nuclear reactors, high-energy physics labs, medical radiotherapy units, academic research facilities etc. In this work, polymethyl methacrylate (PMMA) matrices doped with neodymium oxide were studied and an extensive evaluation of their gamma-radiation and neutron shielding ability was done. The gamma-ray shielding properties of the polymer matrices were evaluated by Hubbell and Seltzer database using XCOM. Different parameters including mass and linear attenuation coefficient, half and tenth value layer and mean free path were assessed. In addition, the neutron shielding properties were assessed from the fast neutron removal cross-sections. Gamma-ray shielding properties in terms of mean free path for photon energies 356 and 662 keV came out to be superior to the ordinary concrete and commercially available shielding glass RS 253. The polymer matricesalso have better neutron shielding properties than the commonly used neutron shields such as Boron Carbide, Polyethylene grains and ordinary concrete. The studied light-weight and flexible PMMA matrices doped with neodymium oxide can serve as protective gamma-ray and neutron shields for the personnel involved in radiation applications.