Recently several design alternatives have been proposed for interactive Video-On-Demand (VOD) systems to satisfy the increasing performance and quality of service (QoS) requirements. Interval caching is a buffer management technique, which can be implemented in conjunction with other techniques to further improve a VOD server performance. This mechanism exploits the temporal locality of requests to the same movie and tries to serve requests from the cache, thereby enhancing system throughput. Earlier studies have examined interval caching with only normal playback operations and have not considered various interactive VCR functionalities such as fast forward, rewind, and pause. Moreover, the complexity of the problem has confined the evaluation methodology to simulation. In this paper, we present a mathematical model for analyzing the performance of an interactive video server that uses interval caching. The model captures the complex interactions of five different VCR operations and predicts the improvement in system throughput due to interval caching. Validation through simulation shows that the model is quite accurate in predicting performance over a wide range of parameters. The usefulness of the model, as a design tool in studying server performance for varying user-interactivity and system parameters, is demonstrated through several examples.