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A new degradation model for safety cables in nuclear power plants that incorporates the critical antioxidant concentration concept is proposed in order to account for the effect of antioxidants and to simulate several synergisms in various thermal and radiation environments. A chemical reaction scheme is used to represent oxidation reactions via the decomposition of peroxide radicals. The effects of antioxidants are included in this scheme in order to demonstrate critical concentration phenomena. In addition, diffusion equations are added to the reaction rate equations to enable reproduction of diffusion-limited oxidation. Such a degradation model with antioxidant effects is discussed for degradation behaviors in polymers used for safety cables under various dose rates and temperature conditions, and its effectiveness is verified.