Reliable multicast is one of the the important and challenging problems that must be effectively resolved before multicast applications can be fully deployed on the Internet. Most existing reliable multicast schemes focus on source-based multicast trees. They either cannot be directly deployed in core-based multicast trees or may render sub-optimal performance when directly deployed. The major difficulty lies in that an on-tree router on a core-based tree does not know, due to lack of the per-source information, how to direct a retransmission request (NAK) toward the sender or some designated replier router/host. We design and evaluate a reliable multicast scheme for core-based multicast trees, called RMCM. RMCM closely emulates the optimal recovery scenario achieved in the turning point approach. Specifically we define new IP options to carry path information in both data packets and NAKs and design a simple, yet effective scheme to facilitate routers on a core-based tree to properly direct NAKs/replies, even in the existence of clouds (of reliable-multicast-incapable routers). To conduct local recovery in the case of group membership and topology changes, we devise a mechanism that selects designated hosts (called repliers) which are most likely to have the requested packet and to which NAKs will be forwarded. We also devise a delayed ACK approach so that both sources and repliers can purge data packets that have been received by all the group members. The event-driven simulation study indicates that RMCM achieves better performance than most existing repair-based reliable multicast schemes, in terms of NAK implosion control, recovery latency, recovery isolation, and capability to deal with clouds. Finally, our experiences with implementing RMCM on FreeBSD 2.2.8 show that the add-on overheads to routers are reasonably small.