Peer-to-peer systems have quickly become a popular way for file sharing and distribution. In this paper, we focus on the subsystem consisting of peers and their actions relative to a specific file and develop a simple theoretical file-centric model for the subsystem. We begin with a detailed model that tracks the complete system state. To deal with the large system state space, we investigate a decomposed model, which not only greatly reduces the complexity of solving the system, but also provides a flexible framework for modeling multiple classes of peers and new system features. Using the model, we can study performance measures of a system, such as throughput, success probability of a file search, and number of file replicas in the system. Our model can also be used to understand the impact of user behavior and new system features. As examples, we investigate the effect of freeloaders, holding-enabled downloading and decoys in the paper.