Nowadays peer-to-peer (P2P) overlay networks are widespread due to their numerous advantages. In P2P streaming networks the main measures to estimate the video playback quality are playback continuity and startup latency. Most analytical models suggest approximate formulas for playback quality measures or algorithms for different chunk download strategies. In this paper, we develop the discrete Markov chain model of the data exchange process between users in P2P streaming network with buffering mechanism. Unlike most of the existing models, we get the exact formulas to calculate the transition probability matrix for the discrete Markov chain. That let us develop a numerical method for the evaluation of playback continuity in P2P streaming network. © 2013 Springer-Verlag.