Alpine glaciers are shrinking and rapidly loosing mass in a warming climate. Glacier modeling is required to assess the future consequences of these retreats on water resources, the hydropower industry and risk management. However, the performance of such ice flow modeling is generally difficult to evaluate because of the lack of long-term glaciological observations. Here, we assess the performance of the Elmer/Ice full Stokes ice flow model using the long dataset of mass balance, thickness change, ice flow velocity and snout fluctuation measurements obtained between 1979 and 2015 on the Mer de Glace glacier, France. Ice flow modeling results are compared in detail to comprehensive glaciological observations over 4 decades including both a period of glacier expansion preceding a long period of decay. To our knowledge, a comparison to data at this detail is unprecedented. We found that the model accurately reconstructs the velocity, elevation and length variations of this glacier despite some discrepancies that remain unexplained. The calibrated and validated model was then applied to simulate the future evolution of Mer de Glace from 2015 to 2050 using 26 different climate scenarios. Depending on the climate scenarios, the largest glacier in France, with a length of 20 km, could retreat by 2 to 6 km over the next 3 decades.