The degradation (e.g., wear, stress corrosion cracking, and fatigue) of nuclear safety systems is an inherently irreversible process, which will lead to system failure when the accumulated damage reaches a threshold level, resulting in catastrophic consequences. Therefore, it is essential to understand and model the degradation behavior of nuclear safety systems to predict and prevent potential failures and thus effectively avoid subsequent losses. This paper proposes a multi-state degradation model for multi-component nuclear safety systems, considering the dependency among the degradation processes and the effect of random shocks. The degradation processes of the system were modeled by the Semi-Markov process. The arrival of random shocks obeys a Poisson process. The transfer kernel function of the holistic model was derived, based on which the Monte Carlo algorithm for estimation of the system reliability was developed. Based on a simple case, the correctness of the proposed model is verified. The model is applied to the reliability analysis of one sub-system of the residual heat removal system of a nuclear power plant.