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Multicast involves transmitting information from a single source to multiple destinations, and is an important operation in high-performance networks. A k-fold multicast network was previously proposed as a cost-effective solution to provide better QoS functions in supporting multicast communication. To give a quantitative basis for network designers to determine the suitable value of system parameter k under different traffic loads, in this paper we propose an analytical model for the performance of k-fold multicast networks under Poisson traffic. We first give the stationary distribution of network states and then derive the throughput and blocking probability of the network. We also conduct simulations to validate the analytical model and the results show that the analytical model is very accurate under the assumptions we make. The analytical and simulation results reveal that by increasing the fold of the network, network throughput increases almost exponentially when the fanouts of multicast connections are relatively small compared to the network size.