It is expected that an increasing proportion of the precipitation will fall as rain in alpine catchments in the future. Consequently, snow storage is expected to decrease, which, together with changes in snowmelt rates and timing, might cause reductions in spring and summer low flows. The objectives of this study were (1) to simulate the effect of changing snow storage on low flows during the warm seasons and (2) to relate drought sensitivity to the simulated snow storage changes at different elevations. The Swiss Climate Change Scenarios 2011 data set was used to derive future changes in air temperature and precipitation. A typical bucket‐type catchment model, HBV‐light, was applied to 14 mountain catchments in Switzerland to simulate streamflow and snow in the reference period and three future periods. The largest relative decrease in annual maximum SWE was simulated for elevations below 2,200 m a.s.l. (60–75% for the period 2070–2099) and the snowmelt season shifted by up to 4 weeks earlier. The relative decrease in spring and summer minimum runoff that was caused by the relative decrease in maximum SWE (i.e., elasticity), reached 40–90% in most of catchments for the reference period and decreased for the future periods. This decreasing elasticity indicated that the effect of snow on summer low flows is reduced in the future. The fraction of snowmelt runoff in summer decreased by more than 50% at the highest elevations and almost disappeared at the lowest elevations. This might have large implications on water availability during the summer.