According to the expansion of broadband access network, the volume of streaming media contents, such as movies or music, is rapidly increasing in the Internet. Very high and sharply fluctuated bit rates are needed to deliver streaming contents. Statistical multiplexing gain must be predicted precisely to achieve required quality delivery cost effectively. Statistical multiplexing gain of Streaming media contents is said to be small. In this paper, we examine statistical gain of a RealMedia content and evaluated the bandwidth to deliver multiplexed RealMedia contents in required quality. Effective bandwidth is defined as bandwidth which is needed to deliver multiplexed contents in required quality. From simulation results, statistical gain of RealMedia Contents is very high if the low quality delivery (5% data loss) is permitted. If high quality delivery (under 1% data loss) is required, statistical multiplexing gain is smaller than the gain in low quality delivery. Traffic of Streaming media contents is said to be long-range dependent. Several analytical formulas to predict effective bandwidth are proposed. Those formulas are derived from analyses of long-range dependent models. In this paper, we check the accuracy of the Norros formula derived from FBM model analysis. Effective bandwidth calculated by the Norros formula is somewhat pessimistic. This result seems to represents that the bit rates of the RealMedia content seems to be more short-range dependent than FBM.