The increasing need for structures to withstand extreme loading conditions, such as blast, has driven research into enhancing the dynamic performance of reinforced concrete (RC) buildings. This study focuses on the innovative use of recycled rubber and steel fibers to improve blast resistance in RC beams, addressing both structural resilience and sustainability. Incorporating recycled rubber not only promotes eco-friendly construction but also enhances the dynamic response of RC beams under blast loads. A comprehensive numerical investigation was performed using validated finite element (FE) models in LS-DYNA, based on UFC-3-340 standards, to assess blast pressure and material response. The models included varying rubber content (5%–20%) and compared three blast simulation methods: load blast enhanced (LBE), arbitrary Lagrangian–Eulerian (ALE), and a coupled approach. Results showed that rubberized steel fiber concrete with up to 10% rubber content offers the best balance of toughness, energy absorption, and structural integrity under dynamic loading.