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Current and future shrinking of mountain glaciation in High-mountain Asia has been in the focus of research activities during the last several decades. Rivers originating in the Inner Tien Shan in Kyrgyz Republic are highly important for several developing countries with growing economies and population, and, therefore, water consumption. Mountain glaciation is one of the main sources of fresh water in the region, contributing essentially to the total river run off especially in dry years. We employ a 3-d higher-order mathematical model (Furst et al., 2011; Zekollari et al., 2013) coupled to a surface mass balance model to reproduce evolution of Sary-Tor Glacier located in Ak-Shiyrak Massif, Inner tien Shan, under changing climatic conditions. For calibration and validation of the model we use results of measurements in snow pits and on ablation stakes during the years 2014-2016. A series of ten prognostic numerical experiments of 90 model years duration was performed. As a climatic forcing, we used surface air temperature and precipitation records on the weather station Tien-Shan-Kumtor located in the vicinity of the glacier. In the schematic scenarios, average daily surface air temperature grows with gradients 0-4 degC/100 yr. Present-day glacier configuration is in imbalance with the climate of 2014-2016. As a result, its area and volume proceed to decrease until equilibrium is achieved after several tens of model years. Under extreme rate of temperature increase (+4 degC/100 yr) Sary-Tor almost diminishes by the end of experiments. Glacial run-off rapidly decreases after initial growth in the first half of the prediction period. Mathematical model inevitably contains simplifications of the real natural conditions. Nevertheless, obtained results will be useful in prognostic water balance calculations in the key region for the country's water supply.