In this paper an approximate numerical solution for a multiclass preemptive priority single server queue is developed. The arrival process of each class follows a Poisson distribution. The service time distribution must have a rational Laplace transform, but is otherwise arbitrary and may be different for different classes. The work reported here was motivated by a desire to compute the equilibrium probability distribution of networks containing preemptive priority servers. Such networks are frequently encountered when modeling computer systems, medical care delivery systems and communication networks. We wish to use an iterative technique which constructs a series of two station networks consisting of one station from the original network and one “complementary” station whose behavior with respect to the original station mimics that of the rest of the network. At each iteration, it is necessary to compute the equilibrium probability distribution of one or more preemptive priority queues.