Reinforced concrete (RC) structures are generally designed to carry quasi-static gravity loads through almost indispensable components namely slab, however, it may be subjected to high intense loads induced from the impact of projectiles generated by the tornado, falling construction equipment, and also from accidental explosions during their construction and service lifespan. Impacts due to rock/boulder falls do occur on the structures located especially in hilly areas. Such loadings are not predictable but may cause severe damage to the slab/structure. It stimulates structural engineers and researchers to investigate and understand the dynamic response of RC structures under such impulsive loading. This research work first investigates the performance of 1000 × 1000 × 75 mm3 conventionally reinforced two-way spanning normal strength concrete slab with only tension reinforcement (0.88%) under the concentric impact load (1035 N) using the finite element method based computer code, ABAQUS/Explicit-v.6.15. The impact load is delivered to the centroid of the slab using a solid-steel cylindroconical impactor (drop weight) with a flat nose of diameter 40 mm, having a total mass of 105 kg released from a fixed height of 2500 mm. Two popular concrete constitutive models in ABAQUS namely; Holmquist-Johnson-Cook (HJC) and Concrete Damage Plasticity (CDP), with strain rate effects as per fib MODEL CODE 2010, are used to model the concrete material behavior to impact loading and to simulate the damage to the slab. The slab response using these two models is analyzed and compared with the impact test results. The strain rate effect on the reinforcing steel bars has been incorporated in the analysis using the Malvar and Crawford (1998) approach. A classical elastoplastic kinematic idealization is considered to model the steel impactor and support system. Results reveal that the HJC model gives a little overestimation of peak displacement, maximum acceleration, and damage of the slab while the predictions given by the CDP model are in reasonable agreement with the experimental test results/observations available in the open literature. Following the validation of the numerical model, analyses have been extended to further investigate the damage response of the slab under eccentric impact loadings. In addition to the concentric location (P1) of the impacting device, five locations on a quarter of the slab i.e., two along the diagonal (P2 & P3), the other two along the mid-span (P4 & P5), and the last one (P6) between P3 and P5, covering the entire slab, are considered. Computational results have been discussed and compared, and the evaluation of the most damaging location(s) of the impact is investigated. It has been found that the most critical location of the impact is not the centroid of the slab but the eccentric one with the eccentricity of 1/6th of the span from the centroid along the mid-span section.