We consider the problem of maximizing the lifetime of a given multicast connection in wireless networks that use directional antennas and have limited energy resources. We first provide a globally optimal solution to this problem for the special case of using omnidirectional antennas. This graph theoretic approach provides insights into the more general case of using directional antennas, and inspires us to produce two heuristic algorithms. Experimental results show that minimum total power consumption does not guarantee maximum lifetime for either broadcasting or multicasting, and our algorithms outperform the group of minimum-energy multicast algorithms significantly.