West Africa is certainly the region where the challenges raised by global change and its impact on the water cycle appear to be the most critical. Against this backdrop of climate variability and change, as well as an increase in water use linked to population growth and improved living conditions, understanding and forecasting the variability of river flows is now a major challenge for improving water resource management. With a view to better anticipation of hydrological variability, a good knowledge of the past is a fundamental step, providing both a better understanding of the hydrological functioning of the basin and a perspective for future hydro-climatic projections. The aim of this study is to analyze the rainfall elasticity of flows over a 100-year period (1921–2020) in Senegal's main hydrosystems: the Senegal, Gambia and Casamance rivers. The elasticity is therefore a simple estimate of the sensitivity of long-term streamflow to changes in long-term rainfall, and is particularly useful as an initial estimate of climate change impact in land and water resources projects. The rainfall elasticity of streamflow is estimated here using a nonparametric estimator. The results obtained show that the elasticity of flows to rainfall is 2.38 for Casamance river basin and range between 1.04 to 2.12 in the Gambia, between 1.92 to 2.76 in the Senegal river basin. These results provide the operational world with simple tools for assessing the impact of climate change on water resources.