The fabric of polar ice exhibiting orthotropic symmetry (i.e., three orthogonal planes of reflexional symmetry) is described by a continuous orientation distribution function (ODF) which represents the density of grains whose c axes have a given orientation. For a given ODF, the constitutive law of such anisotropic ice is obtained by a homogenization procedure based on the assumptions that the ice single crystal behaves as a linear transversely isotropic material and that the grains experience a uniform state of stress. Under loading conditions which respect the symmetries of orthotropy, the evolution of the macroscopic behavior of a polycrystal of ice, as well as the evolution of its fabric, are fully determined by analytical expressions. The solution for a transversely isotropic polycrystal is deduced as a reduction from the orthotropic case. In this special configuration, the results from the present model are compared to fabric measurements made by Thorsteinsson et al. <1997> on the GRIP ice core. ¿ 1999 American Geophysical Union