Under certain conditions the strontium isotope ratio in the water of a semi-enclosed basin is known to be sensitive to the relative size of ocean water inflow and river input. Combining Sr-isotope ratios measured in Mediterranean Late Miocene successions with data on past salinity, one can derive quantitative information on the Mediterranean hydrological budget at times before and during the Messinian Salinity Crisis (MSC). Previous studies obtained this hydrological budget by inverting the salinity and strontium data with steady state solutions to the conservation equations of salt, strontium and water. Here, we develop a box model with a time-dependent set of equations to investigate the coeval evolution of salinity and Sr ratios under different water budgets, gateway restrictions and riverine Sr characteristics. Model results are compared with the salinity and strontium ratio data from the Mediterranean. With a present-day water budget, strontium ratios in the Mediterranean never reach the observed Messinian values regardless of gateway restriction and water budget. However, a model with tripled river input, as inferred for the Late Miocene, is able to reproduce the Sr ratios observed. The onset of the MSC can be explained with a simple restriction of the gateway(s) between the Mediterranean and Atlantic. Lower Evaporite gypsum formed in a basin with less outflow to the Atlantic than modeled in previous studies because of the large Late Miocene river input. Evaporite thicknesses predicted by our model and consistent with the Messinian Sr ratios are on the low end of the thickness range inferred from seismics.