In a video server environment, some video objects (e.g., movies) are very large and are read sequentially. Hence it is not economical to cache the entire object. However, caching random fractions of a multimedia object is not beneficial. Therefore, traditional cache management policies such as LRU are not effective. The sequential access of pages can be exploited by caching only the intervals between two successive streams on the same object, i.e., by retaining the pages brought in by a stream for reuse by a closely following stream and subsequently discarding them. In contrast to the movie-on-demand workload, an interactive workload is composed of many short video clips (e.g., shopping). Hence, concurrent access to the same video chip will be infrequent and interval caching policy will not be effective. In this paper, we propose a Generalized Interval Caching policy that caches both short video objects as well as intervals or fractions of large video objects. To study the efficacy of the GIC policy, we also propose a model for mixed short interactive and long video workloads. The proposed policy is shown to effectively reduce disk overload and hence to increase the capacity of the video server.