During the reel-lay installation, the pipeline undergoes multiple cycles of plastic bending, resulting in a highly complex stress state due to interactions with the reel, aligner, and straighteners. Accurate prediction and control of the pipeline’s structural response are crucial to preventing local buckling and instability. In this study, uniaxial tensile and cyclic loading tests were conducted on materials used in reel-lay installation to determine their parameters. The material response was then fitted using both the isotropic hardening model and the Chaboche model. Based on the actual parameters of China’s first reel-lay vessel, “Shenda,” a full-process finite element model was developed in ABAQUS to simulate the pipeline’s winding, unwinding, and straightening stages. Time-history curves of key parameters, such as curvature and axial strain, were obtained, and the pipeline’s deformation characteristics were analyzed throughout the process. The effects of the isotropic and Chaboche models on the pipeline’s bending moment, stress, and accumulative plastic strain were also investigated. The results indicate that the Chaboche model generally yields lower bending moment, stress, and plastic strain throughout the process, while the isotropic model produces higher values. Designing pipeline parameters based on the isotropic model may lead to overly conservative outcomes.