Efficient utilization of network resources is essential in the provision of quality multimedia services. Different approaches have been proposed to shape the multimedia streams as a transmission schedule with smoothed traffic burst. In this paper, we concentrate on the problem of efficient use of bandwidth and client buffer. For this purpose, an optimal transmission schedule is proposed to provide the minimal allocation of the bandwidth and maximal utilization of the client buffer. Simulation results show that the shaping results obtained can dynamically adjust the transmission rate according to the buffer packet sizes and playback rates at the client to avoid the loss of packets, and at the same time achieve the minimal bandwidth allocation and maximal utilization of the client buffer.