This paper presents an analytical study of a two-stage production system with provision for storage of intermediate product. Strict limits are placed on the size of the intermediate product inventory, and on the rates at which product can be moved into or out of inventory. Exponential service times are assumed at stage one and Erlang distributed service times are assumed at stage two. The problem is solved by formulation as a Markov process, and the impact of the inventory constraints on the production rate of the line is investigated. The problem of balancing the system is considered at some length.