To address two critical challenges in the numerical modeling of precast segmental structures—namely, post-tensioned prestress simulation and adhesive joint representation—this study proposes a refined finite element modeling approach. This method incorporates a nearest point matching algorithm during prestress application, resolving issues such as modeling complexity and low computational efficiency in traditional tendon–concrete node matching. For adhesive joint simulation, a cohesive contact element based on fracture mechanics is adopted, enabling the characterization of tensile-shear coupled failure under combined loading conditions. To validate the method, a precast segmental prestressed cap beam from a real-world project was analyzed under prestressing and service load scenarios. The results demonstrate that the proposed approach is efficient, rational, and practically applicable, providing reliable technical support for high-fidelity numerical simulations of prefabricated structures.