This paper addresses the problem of finding the worst case end-to-end delay and buffer occupancy bounds in ATM networks with rate-controlled, non-work conserving servers. A theoretical framework is constructed to analyze such servers in isolation and in tandem. The analysis is based on a simple fluid model, but care is taken so that the computed delay and buffer occupancy values are upper bounds on actual values. A simple algorithm is presented to perform these calculations in linear time. Simulation results compare the computed worst case delays with the actual delays obtained on some simple network topologies. The algorithm is found to predict node delays well for bursty input traffic, but poorly for smooth input traffic. Buffer requirements are predicted well in both cases.