This paper introduces the circulating processor model for parallel computer systems. The circulating processor model is a product form queuing network model where the processors are allowed to circulate between the parallel applications instead of the more traditional circulating task model. Certain behaviors of parallel systems are better captured using this new approach. The circulating processor model may be load dependent or load dependent. The load dependent circulating processor model is exact for systems which contain a single parallel application. An exact error is calculated for the load independent circulating processor model for systems which contain a single parallel application. The load dependent circulating processor model is a good approximation to the actual system in the case of multiple parallel applications. The load dependent circulating processor model compares favorably to the traditional circulating task model.