This thesis presents a comprehensive literature review on the numerical and analytical modeling of wellbore integrity during CO₂ injection, with the goal of ensuring long-term containment safety in geological carbon storage (GCS) projects. The wellbore–cement–formation system is a critical component in CO₂ sequestration operations, and its mechanical and chemical stability under dynamic subsurface conditions is vital to preventing leakage pathways. The review begins with analytical stress models, including classic elastic solutions and thermally induced stress fields, to evaluate the failure risk under CO₂ injection pressures and temperatures. Numerical simulations—primarily using Finite Element Method (FEM) frameworks—are then discussed to assess stress evolution, damage zones, and fracture propagation, with particular focus on cement sheath degradation due to carbonation, pressure cycling, and thermal mismatch.