Modeling the evolution of glaciers and ice sheets under climate variability requires accurate estimation of ice flow velocities by numerical models. One of the most challenging components of these models is the representation of basal sliding at the rock-ice interface, generally described by relationships between stress and sliding speed. These relationships are mainly derived from laboratory experiments and theoretical studies, and their ability to represent nature still needs to be evaluated. Because direct observation beneath glaciers and ice sheets is difficult, few studies have attempted to validate sliding models from natural scale observations. In this context, our study provides a rare constraint, based on observations on an alpine glacier, on the law that should be used to model glacier sliding on clean bedrock (so-called hard-bed glaciers). We show that a simple power law performs well in explaining long-term glacier behavior for a power exponent of ∼3.1. We suggest that this exponent should be adopted in non-linear power laws incorporated into ice flow models that perform future projections of hard-bedded glaciers and ice sheet evolution.