Video on demand (VOD) is expected to become one of the most important and successful services to be offered on emerging technologies. There is not just an interest in the delivery of digital video for home entertainment purposes, but there are also several educational and commercial benefits from this service. However, for this service to become viable, it is important that the video servers meet the demanding data rates and real time performance requirements imposed by video. Interval caching has been proposed as a cost effective way of improving the throughput of a server, but all previous studies on interval caching have used simulation. With numerous parameters and their complex interplay affecting the performance of interval caching, it is infeasible to consider a full factorial experiment with simulation. The paper presents an analytical model for interval caching on video servers. The model has been extensively validated over a range of client requests, video data and server parameters. In addition, the model has been generalized to accommodate variable lengths of video data stored at the server. Using this model, the impact of different parameters has been studied on the performance of interval caching scheme.