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In this paper, we tackle the multicast problem with the consideration of the interference between multicast trees in multi-radio multi-channel wireless mesh networks (MR-MC WMNs). We consider a dynamic traffic model, i.e., multicast session requests arrive dynamically without any prior knowledge of future requests. Each node in the network acts as a Transit Access Point (TAP), and has one or multiple radios tuned to non-overlapping channels. We prove that in MRMC WMNs, the minimum cost multicast tree (MCMT) problem, i.e., finding the multicast tree with minimum transmission cost, is NP-hard. We then formulate the problem by an Integer Linear Programming (ILP) model to solve it optimally, and propose a polynomial-time near-optimal algorithm, called Wireless Closest Terminal Branching (WCTB), for the MCMT problem. To alleviate the interference between multicast trees (sessions), we present a polynomial-time algorithm that computes the minimum interference minimum cost path in MR-MC WMNs, and integrate it into WCTB without altering the performance bound of WCTB on the tree cost. The experimental study shows that the tree cost produced by WCTB is very close to the optimal and that the proposed algorithm for interference alleviation is effective. To the best of our knowledge, this is the first paper that studies the MCMT problem in MR-MC WMNs.