The complex topography of the Alps makes detailed hydrological modelling a real challenge. It is yet an essential task to improve the insight of hydrological processes in the context of intensification of renewable energy use and under the constraints of climate change. In this perspective and as a case study, the runoff of a small highly glacierized basin in the Swiss Alps – namely the Findelen catchment area – has been modelled with a hydrological model (Routing System 3.0; RS3.0). It is a conceptual model, based on object-oriented programming and it computes snow-melt, glaciers, infiltration and runoff processes. As input, it requires hourly air temperatures and precipitation, and the geomorphologic features of the catchment area and glacier. RS3.0 has proven to be very efficient in reproducing discharge. To evaluate the impacts of climate change on runoff – the final objective of the study addressed in a companion paper – a stochastic meteorological data generator has been developed to reproduce a sequence of air temperature and precipitation over more than one century. In this way, a continuous series of daily discharge values has been simulated by RS3.0 with the stochastic input data. This methodology has also enabled an assessment of the glacier response time to a stable climate. Indeed, if the climatic conditions of the standard reference period 1961-1990 were to be preserved throughout the 21st century, the simulation shows that the watershed would be slow to adapt: the glaciers would be balanced with the atmospheric conditions and the water discharge would reach a lower stable value in more than 40 years. However, the glacierized area would lose only 3.5% of its surface.