With increase in concern for reliability in the current and next generation of Multiprocessors System-on-Chip (MP-SoCs), multi-computers, cluster computers, and peer-to-peer communication networks, fault-tolerance has become an integral part of these systems. One of the fundamental issues regarding fault-tolerance is how to efficiently route a faulty network where each component is associated with some probability of failure. Adaptive fault-tolerant routing algorithms have been frequently suggested in the literature as means of improving communication performance and fault-tolerant demands in computer systems. Also, several results have been reported on usage of fault rings in providing detours to messages blocked by faults and in routing messages adaptively around the rectangular faulty regions. In order to analyze the performance of such routing schemes, one must investigate the characteristics of fault rings. In this paper, we derive mathematical expressions to compute the probability of message facing the fault rings in the well-known mesh interconnection network. We also conduct extensive simulation experiments using a variety of faults, the results of which are used to confirm the accuracy of the proposed models.