In this paper, we present a capacity analysis of an automated transportation system in a flexible assembly factory. The transportation system, together with the workstations, is modeled as a network of queues with multiple job classes. Due to its complex nature, the steady‐state behavior of this network is not described by a product‐form solution. Therefore, we present an approximate method to determine the capacity of the network. We first study a number of key elements of the system separately and subsequently combine the results of this analysis in an Approximate Mean Value Analysis (AMVA) algorithm. The key elements are a buffer/transfer system (the bottleneck of the system), modeled as a preemptive‐repeat priority queue with identical deterministic service times for the different job classes, a set of elevators, modeled as vacation servers, a number of work cells, modeled as multi‐server queues, and several non‐accumulating conveyor belts, modeled as ample servers. The AMVA algorithm exploits the property that the initial multi‐class queueing network can be decomposed into a sequence of single‐class queueing networks and hence is very efficient. Comparison of numerical results of the AMVA algorithm for the throughputs for the different job classes to simulation results shows that the AMVA algorithm is also accurate. For several series of instances, the maximum relative error that we found was only 4.0%.