This paper proposes a Client-Agent-Server model (CAS model) which can decrease the work load of the client by adding agent processors to the Client-Server model and presents an approach to parallel test generation for logic circuits on the CAS model. In this paper, we consider the fault parallelism in which a cluster of faults will be allocated from the client processor to an agent processor and from an agent processor to a server processor for the CAS model. Hence, we have to consider two granulatities ; one is the size of the cluster between the client and agents, and the other is the size of the cluster between agents and severs. We formulate the problem of test generation for the CAS modle and analyze the optimal pair of granulatities in both cases of static and dynamic task allocation. Finally, we present experimental results based on an implementation of our CAS model on a network of workstations using the ISCAS'89 benchmark circuits. The experimental results are very colse to the analytical results which confirms the existence of an optimal pair of granularities that minimizes the total processing time for benchmark circuits as well as analysis.