[Purposes] This paper aims to identify the key parameters influencing the impact damage of reinforced concrete (RC) members encased with rubber concrete, and to clarify the influence of these parameters on the dynamic response and failure modes of the members. [Methods] Drop-weight impact tests were conducted on six RC members encased with rubber concrete to obtain typical damage characteristics. A finite element (FE) model was developed and validated using the experimental results. Parametric analyses were then performed to investigate the effects of axial compression ratio, impact velocity, and impact mass. Damage levels were classified using a section-based damage factor. [Findings] The axial compression ratio, impact velocity, and impact mass were identified as the key factors affecting the impact damage of RC members encased with rubber concrete. A lower axial compression ratio enhances the structural stability, whereas a higher axial compression ratio tends to induce premature shear failure. An increase in impact velocity significantly elevates the kinetic energy, causing localized cracks to rapidly evolve into severe damage. Under a constant impact velocity, an increase in the hammer mass intensifies the inertial effects, leading to more concentrated local damage and exacerbated global failure. [Conclusions] The developed FE model demonstrates high computational accuracy and is suitable for analyzing the impact damage behavior of RC members encased with rubber concrete. The findings provide a useful reference for practical engineering applications.