A model for simulations of the ice microstructure evolution during its deformation is presented. Several competing processes are considered which lead to the development of anisotropic crystal c axes orientation distribution. Existing theories of the plastic deformation and recrystallization dynamics are combined in a discrete algorithm based on the cellular automata approach. We simulate the evolution of the fabric and texture, that is, orientations and sizes of single crystals of polycrystalline ice which experiences uniaxial compression, the loading condition close to that at the summit of the Greenland Ice Sheet. The results of our simulations are in a good qualitative agreement with the data obtained from the Greenland Ice Core Project ice core drilled at this location.