Free riding in peer-to-peer (P2P) systems means a peer utilizing other peers' network resources without contribution. Recent empirical studies have identified serious free riding problem in P2P streaming systems which will cause severe performance degradation. However, scarce existing work is focused on theoretical modeling and analysis of free riding problem. In this paper, we present a two-class fluid model to model and analyze the free riding problem in P2P streaming systems. With this model, we provide a quantitative analysis of the effect of free riding on P2P streaming systems particularly in the steady state with two scenarios: one without seeders and the other with seeders. The steady state analysis results show that (i) both honest peers and free riders have a much lower download time in the scenario with seeders than that without seeders, and thus it is essential to introduce mechanisms to incentivize the seeders to stay in the system, and (ii) free riders can benefit greatly from the streaming server and the seeders, and thus it is important to introduce differentiated service mechasisms for the server and seeders in P2P streaming systems.