Macroscopic elastic constants for multiphase polycrystalline materials are calculated within a two-level constitutive model. The transition from microscopic to macroscopic elastic constants is based on the principles of averaged relationships between the orthogonality of stress and strain tensor fluctuations and the mismatch between macroscopic measures and their corresponding microscopic counterparts. Numerical studies are conducted for polycrystals with a cubic crystal lattice. The numerical results obtained demonstrate nonlinear laws for the variation of macroscopic elastic constants depending on the phase weight.