In response to the important role that multicasting plays in wireless mobile multihop ad hoc networks, we study in this paper the reliability of the on-demand multicast routing protocol (ODMRP) in terms of the delivery of data packets. Using GloMoSim 2.0, the simulation results have shown that using ODMRP, the average miss ratio does not always increase with increasing the speeds of mobility of the mobile hosts in the ad hoc network. Instead, there is a "sweet spot" of values of the mobility speeds of the mobile hosts. In addition, the average miss ratio decreases with increasing the number of multicast group members, which indicates that ODMRP has more packet delivery capabilities for denser multicast groups.