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The estimate of the age of the ice-firn thickness located on the western plateau of Mt. Elbrus (Caucasus, Russia) is obtained. The dating is based on the calculated velocities in the glacier. The three-dimensional full Stokes-flow equations are applied to non-linear viscous flow law to obtain the velocity field. Steady-state conditions are assumed. Since large parts of the glacier consist of firn rather than pure ice, a compressible snow/firn rheological law is applied. The results are checked against the ice core dating.