A theory to determine the complete tensor of elastic moduli of general
ly anisotropic polycrystalline ice and its temperature dependence from
the elastic properties of single ice crystals is presented in this pa
per. The model. expressed in closed-form, predicts the upper and lower
bound limits of the elastic moduli for such polycrystals by generaliz
ing the methods of Voigt (1910) and Reuss (1929), respectively, that w
ere developed for isotropic aggregates. This involves obtaining the sp
atial average of the elastic moduli and compliances of individual crys
tals of ice by weighting them with the relative frequency of their ori
entations in the anisotropic fabric. Single ice crystals possess an op
en hexagonal structure and are transversely isotropic in their elastic
properties. The theory is then applied to predict the elastic constan
ts of transversely isotropic S1 and S2 ice, and orthotropic S3 ice. Th
e predicted upper and lower bound limits are in excellent agreement wi
th available experimental data.