Prolonged operation of light water reactors increases fast neutron exposure to the concrete biological shield (CBS) and reactor pressure vessel (RPV) supports, degrading near‑surface concrete and altering load transfer during accidents. A unified, multi‑hazard probabilistic framework is developed and applied to quantify the reliability of these structures under a design‑basis loss‑of‑coolant accident (LOCA), a safe‑shutdown earthquake (SSE), and their combination. Strength limit states are formulated for the CBS and RPV support system. Capacity models, informed by multi-physics, mesoscale simulations, are parameterized by irradiation‑induced damage depth and steel reinforcement ratio. Accident demand models incorporate LOCA cavity pressures and jet forces consistent with system level thermal-hydraulic analyses and code‑based seismic base shear. Uncertainties in material properties, degradation depth, demands, and modeling are represented with statistically consistent distributions, and reliability indices and failure probabilities are estimated via Monte Carlo simulation with Latin hypercube sampling. The framework delivers reliability indices and failure probabilities for plain, minimally reinforced, and fully reinforced configurations and identifies the most critical limit states for each. These findings support risk‑informed surveillance and life‑extension decisions, highlighting the need to track irradiation damage depth in the CBS, prioritize reinforcement and anchorage details in high‑flux regions, and explicitly evaluate coupled accident scenarios in aging plants.