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The Universal Mobile Telecommunications System (UMTS) network consists of a core network (CN) and a UMTS terrestrial radio access network (UTRAN). The UTRAN offers radio access bearer (RAB) services between the user equipment (UE) and the CN to support mobile multimedia applications with different quality of service (QoS) requirements. Depending on the requested QoS, different types of RABs can be established at the request of the CN. The UTRAN then has to establish and maintain the RAB with the requested QoS. We study the queueing of RABs as a means for improving the bandwidth utilization while minimizing the RAB blocking probability. We develop an analytical model to study the performance for UTRAN with queued RABs in terms of RAB blocking probability and average queueing time of queued RABs. From an analytic point of view, the main contribution of this paper is the introduction of a novel recursion for the computation of the performance measures.