This paper considers a queueing network model for the performance evaluation of a flexible manufacturing system composed of several parallel workstations (machines), each with both limited input and output buffers, where machine blocking is allowed and two automated guided vehicles (AGVs) are used for handling input and output materials. An iterative solution algorithm is exploited to approximate system performance measures such as system throughput and machine utilization. For the approximation, the queueing network is decomposed into individual queues (input queues and an output queue) to analyze each in isolation. Moreover, the output queue (subsystem) composed of finite capacity parallel output buffers and a single server (AGV(O)) is analyzed by using the theory of reversibility. A variety of numerical problems are solved to show the effectiveness of the algorithm in comparison with simulation approach.