Multicast network is widely used for effective communication, transmission and performance optimizations of a network. In this paper, a new model has been developed to determine a suitable value of the fold k of a k-fold multicast network under different traffic loads under Poisson traffic with finite queue at each node. We have derived stationary distribution for the network states and then derived expressions for the network throughput and the blocking probability of the network. It has been found in this research work that the network throughput increases very fast as we increase the fold number. However, at a certain value of the fold, the blocking probability ceases to increase and it remains constant. We have also observed that as the offered traffic is increased, the throughput also increases. Moreover, the system parameter k is increased, the blocking probability decreases. However, after an optimum value of k, the blocking probability remains constant for a particular value of the offered traffic. In fact, in this paper, by evaluating the performance of a k-fold multicast network, our developed model improves the performance of a multicast network.