The stress-strain rate relations for an anisotropic, incompressible viscous body that is orthotropic, transversely isotropic, are drawn from symmetry considerations. This kind of material forms the largest part of polar ice sheets. The 10 parameters entering the rheological law would be extremely difficult to draw from torsion-compression tests, the only ones that are feasible on ice cores. Nevertheless, homogenization allows to infer them from the statistical distribution of the c-axes and only two parameters that are accessible by readily analyzed pure shear tests. Homogenization is done assuming for any crystal embedded in rock ice a rheology that differs from the one of isolated monocrystals and microscopic stresses at the crystal level equal to the macroscopic stress. Both assumptions are argued, in the light of experimental evidence about a single system of active slip planes, very low dislocation velocities, pile-ups at the grain boundaries, and boundary migrations during strain. These migrations destroy the pile-ups, besides allowing the strains in neighbour crystals to be different.