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Traffic jams have been occurring recently on most city street networks. These jams can be avoided by predicting the traffic flow patterns in advance using computers. The reduction of computer time is very important, especially in the case of real-time prediction of traffic flows. This paper develops a special-purpose simulator for calculating road traffic flows. The simulator consists of several transputers and a random number generator. Large and complex street networks are partitioned, and each partition is assigned to a transputer for parallel calculations. The stochastic nature of the traffic is taken into account by using random numbers generated by a random number generator. Some traffic flow patterns are calculated with this simulator. The developed simulator can simulate large and complex street networks using a small amount of computer time. Index Terms - Random number, traffic flow, transputer.