In this paper, we present an efficient scheme for the multicast transmission of the data in the Universal Mobile Telecommunications System (UMTS). We take advantage of the tree topology of the examined network and we introduce the use of Routing Lists (RLs) in the nodes of the UMTS. The adoption of these lists leads to the decrement of the transmitted packets and to the efficient use of network resources in the multicast transmission of the data. We describe in detail the appropriate steps for the successful multicast transfer of data. Furthermore, we analyze the handling of special cases such as user mobility scenarios. Especially, the various handover types are examined along with the Serving Radio Network Subsystem relocation procedure. Finally, we implement our approach in the NS-2 simulator and we present the performance of the multicast mechanism.