Ultrasonic techniques have recently been applied to the texture characterization in polycrystalline aggregates of hexagonal crystals. The basis of this application lies in the relations between the elastic constants _ij of the aggregates, which can be inferred from ultrasonic wave velocity measurements, and the orientation distribution coefficients. This communication presents such relations for aggregates which possess orthotropic material symmetry and hexagonal crystal symmetry for Voigt, Reuss, and Hill averaging methods in a unified and concise representation.