In this paper, we present an analytic model to estimate the performance of cut-through buffered banyan networks with finite buffer size. Two conflict resolution policies are considered in order to resolve conflicts when two packers are destined to the same output link, and their performances are compared. Our analytic model enables analysis of the networks in which buffers are unevenly distributed, i.e., each stage has a different buffer size. It is shown that if buffers are properly distributed in the network, higher throughput and lower delay are possible, although the improvement is considered small. Finally, in order to validate our model, some analytic results are compared to simulation.