Reorientation of individual crystal glide planes, as isotropic surface ice is deformed during its passage to depth in an ice sheet, creates a fabric and associated anisotropy. We adopt an evolving orthotropic viscous law which was developed to reflect the induced anisotropy arising from the mean rotation of crystal axes during deformation. This expresses the deviatoric stress in terms of the strain rate, strain and three structure tensors based on the principal stretch axes, and involves one fabric response function which determines the strength of the anisotropy. The initial isotropic response enters as a multiplying factor depending on a strain-rate invariant and incorporating a temperature-dependent rate factor. The fabric response function has been constructed by correlations with complete (idealized) uniaxial compression and shearing responses for both ‘cold’ and ‘warm’ ice. The possible effects of such fabric evolution are now illustrated by determining steady radially symmetric flow solutions for an ice sheet with a prescribed temperature distribution and subject to an elevation-dependent surface accumulation/ablation distribution, zero basal melting and a prescribed basal sliding law. Comparisons are made with solutions for the conventional isotropic viscous law, for a flat bed, for a bed with a single modest slope hump and for a bed with a single modest slope hollow, for both cold and warm ice.