In this paper, the physical parameters Y elastic constants mewly proposed in our previous paper are applied to polycrystalline materials with hexagonal structure to deduce Y elastic constants thereof and to compare with the x-ray elastic constants of polycrystalline materials of hexagonal structure through calculation of examples. Though the expressions of mechanical elastic constants of polycrystalline materials deduced from the application of Y elastic constants are different from the conclusions of Kneer, the calculaled results for concrete materials are in full compliance.