Gamma-ray shielding materials play a crucial role in nuclear technology, medical physics, and radiation protection, where efficient attenuation of ionizing radiation is required. In this study, the gamma-ray shielding performance of several polymer-based materials, namely polyurethane (PUR), polypropylene (PP), polytetrafluoroethylene (PTFE), polyvinylidene fluoride (PVDF), and polyvinylidene fluoride–hexafluoropropylene (PVDF-HFP), together with silicon carbide (SiC), included as a non-polymeric ceramic reference material, was systematically investigated and compared with conventional lead (Pb) using the MCNPX Monte Carlo code. The shielding effectiveness of each material was evaluated in terms of key radiation interaction parameters, including the mass attenuation coefficient (MAC), half-value layer (HVL), and mean free path (MFP), over a wide photon energy range of 122, 356, 511, 662, 1170, 1275, and 1330 keV, corresponding to commonly used radioactive sources in medical and industrial applications. The obtained results indicate that lead exhibits the highest gamma-ray attenuation capability across the entire energy spectrum, as expected due to its high atomic number and density. Among the investigated materials, SiC demonstrates superior shielding performance compared to the polymers, followed by PTFE, particularly in low and intermediate-energy regions. These materials also show comparatively lower HVL values and shorter mean free paths, indicating improved radiation attenuation efficiency. Overall, the findings suggest that SiC and PTFE-based polymer systems can serve as promising lightweight and non-toxic alternatives to lead for gamma-ray shielding applications, especially in low to medium-energy radiation environments.