Queueing models can be used to evaluate the performance of manufacturing systems. Due to the emergence of cluster tools in contemporary production systems, proper queueing models have to be derived to evaluate the performance of machines with complex configurations. Job cascading is a common structure among cluster tools. Because of the blocking and starvation effects among servers, queue time analysis for a cluster tool with job cascading is difficult in general. Based on the insight from the reduction method, we proposed the approximate model for the mean queue time of a cascading machine subject to breakdowns. The model is validated by simulation and performs well in the examined cases.