The evolution of the Black Sea's salinity after the opening of the Bosporus about 7500 years ago is investigated using a simple two-box model. The model consists of watermass and salt conservation equations, and allows for changes in halocline depth. The paleoceanographic box model is forced by present-day Mediterranean inflow and outflow, and atmospheric forcings. Analytic solutions for the evolution of the box volumes are given. Model salinities reach 90% of their the present-day values in both boxes about 2,500 years after the opening of the Bosporus. The evolution of the salinities is shown to be almost independent of the evolution of the box volumes, and the results are compared with the existing paleoceanographic proxy records.