Abstract. Different flowline thickness distributions and flowline length changes of the Gregoriev Ice Cap were obtained for some surface mass balance histories which can be considered as possible surface mass balances in the future. The ice cap modeling was performed by solving full Stokes equations in the form of one mechanical equilibrium equation in terms of stress deviator components in couple with continuity equation for incompressible substance. The numerical solution was obtained by the finite-difference method. The problem of diagnostic equations stability was overcome by a~compound approximation of the ice surface boundary condition based on the extending of the mechanical equilibrium equation to ice surface points. The problem of stability in the prognostic equation can arise at relatively small grid size in horizontal direction in the case of steep velocity decreasing closely to the ice front and was overcome by introducing the artificial viscosity into the prognostic equation. The basal sliding can arise in the glacier tongue at certain climatic conditions and was introduced through the linear friction law. The correlations between glacier length changes and annual air temperature histories were investigated within the simplified equation in the form of linear dependence of annual air temperature versus the glacier length and time derivation of the length.