The rapid development of P2P technologies and appearing scope of applications involving it will help to solve a lot of optimization problems and improve the QoS for data delivery services. This paper is an extension of previous papers devoted to modelling P2P media streaming service and describes the design and simulation software architecture of P2P streaming network with buffering mechanism for a single media stream. We consider mathematical model in the form of discrete Markov chain taking into account the so-called lag-the time delay of data transfer between peers, download strategies and possible peer groups according to distances between them. Program algorithm is presented using UML activity diagram and the simulation results are shown. © ECMS Valeri M. Mladenov, Petia Georgieva, Grisha Spasov, Galidiya Petrova (Editors).