Asychronous Transfer Mode (ATM) provides the means to transport different types of bursty traffic such as voice, video, and bulk data. To handle more efficiently the traffic sources and to increase the bandwidth utilization as much as possible, flexible statistical multiplexing schemes must be adopted for the ATM networks. This paper presents an efficient computational procedure to calculate the queue state distribution in a finite buffer queueing system with a number of independent input sources, and the cell loss probability is exactly calculated with the use of this recursion computation method. The cell loss probability is related to a ATM multiplexer with a homogeneous ON-OFF source is also investigated through numerical examples.