The paper is devoted to the simulation of queueing networks on high performance computer clusters. The objective is to develop a mathematical model of queueing network and simulation approach to the modelling of the general network functionality, as well as to provide a software implementation on a high-performance computer cluster. The simulation is based on a discrete-event approach, object oriented programming, and MPI technology. The model of the queueing networks simulation system was developed as an application that allows a user to simulate networks of rather free configuration. The experiments on a high performance computer cluster emphasize the high efficiency of parallel computing.