With the fast development of computer and network technology, streaming media has attracted more and more attention. The concurrent capacity is a major performance index, especially for media service providers. In the current literature, the concurrent capacity of a server is usually determined through experiments, which can only be done after building a server and are timeconsuming. This paper proposes a method to estimate the concurrent capacity just with the configuration parameters of a server. Due to the fast CPU and high-speed network cards, the bottleneck of the concurrent capacity is the I/O speed, which is determined by both the fast memory and low-speed hard disks in a server. By analyzing the behavior of users, we estimate an upper bound on the percentage of data supplied by the memory, named byte-hit-ratio, under any realistic scheduling policy between the memory and disk for a given memory capacity. Based on the byte-hit-ratio bound, we can obtain an upper bound on the average I/O speed of the server, which is proportional to its concurrent capacity. Our method does not require any actual tests and can guide the design of streaming media servers.