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Some ad hoc network scenarios are characterized by frequent partitions and intermittent connectivity. Hence, existing adhoc routing schemes which assume the existence of end-to-end paths do not work in such challenging networks. Disruption tolerant networking (DTN) technology has been designed for such challenging network environments. Several unicast and multicast routing schemes have been designed for DTNs. However, the existing multicast routing schemes assume a route discovery process that is similar to the existing adhoc network routing approach, and hence will not work well in very sparse network scenarios. Thus, in this paper, we explore an encounter-based multicast routing (EBMR) scheme for DTNs. Our scheme uses fewer hops for message delivery. We present an analytical framework for estimating the delivery performance of the EBMR scheme, and present some analytical and simulation results to show that the EBMR scheme can achieve higher delivery ratio while maintaining high data transmission efficiency compared to other multicast strategies.