Vertically stacked optical banyan (VSOB) networks are attractive for serving as optical switching systems due to the good properties of banyan network structures (such as the small depth and self-routing capability), and it is expected that using the VSOB structure will lead to a better fault-tolerant capability because it is composed of multiple identical copies of banyan networks. Some analytical models have been developed to analyze the blocking behaviors of VSOB networks. However, none of theses analytical models has taken into account the fault-tolerant property of the VSOB networks. In this paper, we conduct the fault-tolerance analysis for the VSOB networks and present an analytical model for the blocking probability of VSOB networks when link faults are taken into account. We also conduct simulation to verify the model. Our analytical and simulation results show that our model can accurately describe the blocking behaviors of the VSOB networks at the presence of link failure. Our model also reveals a fact that by accepting a small link failure probability, the blocking behavior of a VSOB network is very similar to that of a fault-free one, which demonstrates our expectation of good fault-tolerant property of VSOB networks. The model is significant because it provides network developers a quantitative guidance to determine the effects of network failure on the overall blocking behaviors of VSOB networks and initiates a graceful compromise between blocking probability and hardware cost in a faulty VSOB network.