This paper proposes a set of novel multicast algorithms for m-D mesh overlay networks that can achieve shorter multicast delay and less resource consumptions. In contrast to previous approaches, our algorithms partition the group members into clusters in the lower layer, seeking an optimal core (root) to guarantee the minimum routing delay for each cluster and building a shared tree within each cluster to minimize the number of links used. In the upper layer, a shared tree is then constructed using our algorithms to implement the inter-cluster routing. The extended simulation results indicate that the application layer multicast that is constructed by our algorithms is efficient in terms of routing delay and link utilizations as compared with other well-known existing multicast solutions.