The paper addresses the flow control problem in two-level assembly production lines composed of a unique assembly machines and multiple upper level machines. In order to obtain a finished product, the assembly machine needs components produced by different upper level machines. We assume that the production capacity of each machine is constant and the demand is known over the whole problem horizon. Backlogging is not allowed. The flow control problem consists of adjusting the production of the machines in order to minimize the total cost incurred by holding components and finished products. Properties of the optimal solutions are given. Based on these properties, we propose a simple analytical solution.