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In this paper, a method is proposed to compute all the strict minimal siphons (SMS) in an S3PR based on resource circuits. The concepts of A-resource subsets, B-resource subsets, and elementary B-resource subsets are proposed, which play an important role in finding SMS. Moreover, it is proved in this paper that not all the resource circuits can generate SMS and SMS are generated by elementary B-resource subsets. An FMS example is used to illustrate the application of the proposed method.