We consider IP over ATM networking scenario, widely deployed today, where Asynchronous Transfer Mode (ATM) is used as a backbone network to provide high-speed transport for the Internet Protocol (IP) traffic. Telecommunication network carriers and Internet Service Providers (ISPs), that have deployed ATM as their backbone networks, need to model and characterize the IP traffic in order to plan and manage these networks to meet specified performance measures demanded by their customers. This paper addresses the problem of modelling IP traffic that is being transported over links of an ATM network. It provides mathematical models that can be used to take measurement data and translate it into a form that is suitable for various planning and management functions performed by network carriers.