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This paper is concerned with the computation of stationary distributions of priority multiclass queueing networks with multi-sever stations, which are associated with high-speed integrated services packet networks. General product-form solutions are iteratively derived for the networks under certain assumption related to interarrival and service time distributions and theory is established to justify the solutions in several cases. These solutions can be used to conduct performance analysis or as comparison criteria for approximation and simulation studies of large scale networks with multi-processor shared-memory switches. Numerical comparisons with existing Brownian approximating model are given to show the usage and effectiveness of our algorithm.