Developing effective shielding solutions for patients and treatment rooms against the mixed photon and neutron radiation generated by medical linear accelerators (LINACs) remains a longstanding challenge. In this study, we fabricated five polymer-based composite materials incorporating varying weight percentages of photon and neutron attenuators—specifically lead or tungsten combined with boron carbide—as fillers. We evaluated their radiation attenuation performance against gamma-ray and neutron sources to assess their suitability for practical radiation protection applications. Our results indicate that the superior composite (M5) contained 60 wt% tungsten, 7.5 wt% boron carbide, and 32.5 wt% elastomer (35.45% NR, 64.55% CR) and exhibits enhanced shielding properties against both photons and neutrons, highlighting its potential as an effective, lightweight, and versatile shielding material for medical radiation environments.