The third generation cellular network UMTS, provides large opportunities to offer multimedia applications and services that meet end to end quality of service (QoS) requirements in a more efficient way, considering packet data transmission mode. However, this requires us to design an efficient flow control and call admission control (CAC). Design of CAC has special difficulties given that capacity in CDMA varies according with the number of active users and the level of interference. Taking into account the stochastic nature of multimedia traffic and the changes in the available capacity in the CDMA system, an effective capacity request is derived and used to characterize the resources required by each mobile user in order to meet its respective QoS requirements. These requirements are expressed in term of rate and delay constraints in addition to the signal to interference ratio. After setting an effective capacity threshold for the system a linear approximation is used to find the total amount of resources required by all the mobile users already admitted in the system and the new connection request. Packet transmission is considered for both real time and nonreal-time services while a centralized demand assignment algorithm has been implemented in order to provide QoS in the packet level. Computer simulation results are given to demonstrate the performance of the proposed method.