A method and system for transmitting a video stream in an asynchronous transfer mode (ATM) network comprises steps of encoding the video into an MPEG-2 variable bit rate video stream, shaping the encoded variable bit rate video stream to conform to the traffic contract parameters for a Variable Bit Rate (VBR) connection in the network, and transmitting the shaped variable bit rate video stream on the VBR connection based on the traffic contract parameters. For a given network bandwidth, switch buffer space, and equivalent video quality, the network can statistically multiplex a larger number of variable bit rate video streams by maximizing the utilization of the network bandwidth and switch buffer space that the network allocates to each video stream.