The present invention establishes a circuit emulation service (CES) over an internet protocol (IP) network based on properties of the IP network. The CES emulates a circuit from a local interworking function to a remote interworking function. Data that is received at a constant bit rate at the local interworking function is encapsulated into a number of IP packets configured according to the CES. The IP packets are transported from the local interworking function to the remote interworking function according to the CES. In one embodiment, each IP packet also includes data segments for simultaneously encapsulating multiple constant bit rate circuits. In another embodiment, each data segment includes a separate CES circuit header.