The necessity of mitigating carbon dioxide (CO2) emissions to combat global warming has led to exploring carbon capture and storage (CCS) options, such as injecting CO2 into subsurface formations. This research looks into the impact of CO2 injection on the elastic and mechanical properties of carbonate and caprock core samples relevant for geological CO2 storage. Rock samples underwent CO2 injection for certain period of time, and various rock elastic and mechanical properties were measured including P-wave velocity, S-wave velocity, Young's modulus, Bulk modulus, Poisson's ratio, and fracture toughness. Results show a consistent reduction in compressional wave velocity (Vp), Young's modulus, Poisson’s ratio, and fracture toughness following CO2 injection. The study indicates that CO2 sequestration reduces stiffness and elastic properties in both carbonate and caprock formations, with the most notable effects observed in fracture toughness for the case of Limestone-A. The change in fracture toughness is less pronounced in caprock samples as compared to carbonate samples. Seismic data, dependence on these properties, plays a crucial role in monitoring CO2 storage in the subsurface words.