The finite capacity of storage has a significant effect on the performance of a contemporary computer system. Yet it is difficult to formulate this problem and analyze it by existing queueing network models. We present an analysis of an open queueing model with two servers in series in which the second server has finite storage capacity. This network is an exponential service system; the arrival of requests into the system is modeled by a Poisson process (of rate &lgr;) and service times in each stage are exponentially distributed (with rates &agr; and &bgr; respectively). Requests are served in each stage according to the order of their arrival. The principal characteristic of the service in this network is blocking; when M requests are queued or in service in the second stage, the server in the first stage is blocked and ceases to offer service. Service resumes in the first stage when the queue length in the second stage falls to M-1. Neuts [1] has studied two-stage blocking networks (without feedback) under more general statistical hypothesis than ours. Our goal is to provide an algorithmic solution which may be more accessible to engineers.