We present a simulation tool, based on a cellular automaton algorithm developed by D. Ktitarev and others, for the modelling of fabric and texture evolution in polycrystalline ice. the numerical results for the case of vertical uniaxial compression are compared with data obtained from boreholes GRIP–GISP2 in Greenland. A reasonable agreement is obtained, and guidelines are presented for further formulation of more realistic simulations. In particular, we discuss the rise of girdle-type fabrics, as well as the importance of intra- and intercrystalline stresses, temperature and impurity effects on the evolving ice microstructure.