Wellbores play a vital role in CO2 sequestration, underground hydrogen storage, and the extraction of subsurface resources like gas, oil, and geothermal energy. Damage to the wellbore can result in serious challenges, such as loss of zonal isolation, fluid leakage, environmental contamination, sustained casing pressure, and even blowouts. A comprehensive analysis of the wellbore system, encompassing the casing, cement, and surrounding geological formations, is essential for maintaining operational performance, safety, and economic feasibility. However, evaluating wellbore stability using numerical methods remains complex due to the intricate nature of failure mechanisms in subsurface environments and multilayered media. Often, when a crack encounters a material interface in the wellbore, one can expect competition between crack deflection along the interface, arrest, and penetration (Lecampion et al., 2018). In layered media, in addition to material mismatches, geometric features also influence the fracture pattern (Khan et al., 2023). The numerical method used for such applications must facilitate crack nucleation and interactions of a propagating fracture with material interfaces. The phase-field method offers significant advantages in modeling complex cracks, including the ability to simulate crack propagation, branching, and coalescence without predefined crack paths (Ambati et al., 2015). This paper explores the application of the phase-field method, an energy-based technique, to analyze wellbore integrity under conditions such as eccentric casing placement and weakened interface, enabling a more precise and efficient evaluation of wellbore integrity, thereby improving the overall safety and reliability of wellbore operations.