This chapter explores the dynamic response of a novel rubberized ultra-lightweight high-ductility cement composite (RULHDCC), engineered at a density of 1450 kg/m3 with polyethylene (PE) fibers and recycled rubber powder from waste tires. Static and split Hopkinson pressure bar (SHPB) tests reveal that compressive strength decreases with increasing rubber content but is partially recovered by adding PE fibers. The static elastic modulus also decreases with rubber content due to poor interfacial bonding and the low rubber stiffness. The composite exhibited enhanced ductility, attaining 3-5% direct tensile strain, with rubber enhancing toughness and 0.7% PE fibers boosting splitting strength while mitigating strength loss. A validated dynamic increase factor (DIF) model is proposed that surpasses CEB-FIP and Malvar-Crawford predictions by accurately capturing rate-sensitive behavior. Numerical simulations using a calibrated Holmquist-Johnson-Cook (H-J-C) constitutive law accurately simulates crack evolution and failure modes. Simple mathematical formulation was developed for dynamic impact strength (DIS) by using the distinct characteristics of evolutionary algorithms. This synthesis addresses gaps in ultralightweight high ductility cement composite and promotes sustainability through waste utilization, enabling eco-friendly, impact resistant, and resilient infrastructure.