New physical parameters “Y elastic constants" and their physical meanings are proposed at the first time. The Y elastic constants are applied to the polycrystalline materials with cubic system structural single crystals, and they are deduced and compared with the “X-ray elastic constants" of polycrystalline materials with cubic system structural single crystals. The expressions of mechanical elastic constants of polycrystalline materials based on Y elastic constants are in good agreement with that proposed by Krner.