In recent years, the alarming number of terrorist attacks has highlighted the critical need for extensive research aimed at fortifying structures against explosion-induced loads. However, the insufficient energy absorption and brittleness of conventional concrete make it ineffective in withstanding blast loading, encouraging researchers to explore innovative strategies for augmenting the energy dissipation capabilities of construction materials. This study specifically delves into the incorporation of recycled rubber, a sustainable and environmentally friendly solution to the pressing issue of scrap tire disposal. The primary focus of this research revolves around the integration of rubber recycling and steel fibers into concrete, with the ultimate goal of enhancing the dynamic response of reinforced concrete (RC) beams. This novel approach not only contributes to the structural resilience required for resisting blast impacts, but also aligns with eco-friendly practices by reusing recycled rubber. A meticulous numerical investigation was undertaken to comprehensively assess the static and blast response of these augmented beams. The numerical study involved developing finite element (FE) models using ABAQUS version 6.14 for static implicit analysis and LS-DYNA R11 for blast explicit simulations. The ABAQUS model was validated against previous experimental testing for load–displacement and failure patterns. Similarly, the LS-DYNA model was validated for blast pressure in accordance with UFC-3-340 standards and for material response under blast loading, utilizing existing experimental data. The numerical models were designed to accommodate varying weight percentages of rubber, ranging from 5% to 20%, and a consistent 1.0% incorporation of steel fibers. This comprehensive analysis aims to provide valuable insights into the efficacy of these materials in improving the structural integrity and blast resistance of RC beams, thereby contributing to the development of more secure and sustainable construction practices. By reducing the reinforcement ratio in order to meet the minimum code requirements, it became evident that the failures of the rubberized RC beams tended to exhibit ductility on the tension side under static loading. In addition, the increase in the reinforcement ratio correlated with a higher failure load and decreased deflection. Furthermore, the findings indicated an optimal concrete mixture characterized by improved ductility, energy absorption, and blast load capacity, achieved by combining 5–10% rubber with steel fibers.