Utilizing a polymer-based radiation shield offers lightweight, low cost, non-toxic compared to lead and solution for eliminating generated secondary neutrons. Incorporating silicon (i.e., one of the most abundant elements) in new applications, such as shielding, would have an impact on the economy and industry. In this study, seven potential shielding materials, composed of silicon, silicon carbide, and boron carbide embedded ethylene vinyl acetate (EVA) copolymers, are proposed. The shielding performance of these composite materials, including the attenuation coefficients (µ), the mass attenuation coefficients (µm), the half value layer (HVL), the mean free path (MFP), and the radiation protection efficiency (RPE) were examined using photon beams. Measured µm were verified against the calculated values. The averaged agreement was within ±7.4% between the experimental measurements and the theoretical calculation results. The HVL and MFP measured values for the polymer composites were lower than that for the pure EVA polymer, indicating the fillers in the polymers enhanced the shielding performance. The EVA + SiC (30%) and EVA + Si (15%) + B4C (15%) composites required the lowest thickness to stop 50% of the incident photons. The evaluation of experimental results of the RPE revealed that the polymer composites containing SiC (30%), Si (15%) + B4C (15%), or SiC (15%) + B4C (15%) succeeded in blocking 90–91% of X-rays at nearly 80 keV. However, a thicker shield of the proposed composite materials or combined layers with other high-Z materials could be used for higher energies.