A theoretical treatment of on-stream activation analysis is given based on the nuclear and flow phenomena involved. A dilute solution of natural uranium in water is considered for illustrative purposes and to demonstrate the application of the mathematical models developed to a practical analytical problem. However, the underlying principles and the mathematical treatment are quite general and are equally applicable to on-stream activation analysis of similar systems. In a subsequent paper, experimental measurements in uranium and thorium solutions will be reported. It is shown that an arrangement in which continuous plug flow of a fluid stream is irradiated and counted simultaneously will lead to the highest count rate at a given concentration of the element under analysis. Cases of interrupted and well-stirred flow conditions are also studied and compared. Continuous and pulsed irradiation and counting arrangements are also compared and the advantages and shortcomings of each system are discussed.