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In structural reliability engineering, one often encounters situations where the strength of a structure is influenced by the stress, but the stress is irrelevant to the strength. This phenomenon can be called a unilateral dependency of strength on stress. To evaluate structural reliability in such cases, the stress on a structure is proposed to be a discrete random variable, and the stress dependent strength is represented by a discrete random variable that has different conditional probability mass functions under different stress amplitudes. Then a discrete stress-strength interference model with stress dependent strength is presented based on the universal generating function technique. Finally, the effectiveness of this model is demonstrated by an illustrative example.