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Based on the static deformation scheme envisaged by the effective medium theory developed by Zeller and Dederichs [Phys. Status Solidi B 55, 831 (1973)] formally similar to that of the quantum mechanical multiple scattering method, we have deduced a general expression for determining the effective elastic properties of any single component polycrystalline substance. From these general formulas using appropriate symmetry for the component crystallite the expressions for cubic, hexagonal, tetragonal, trigonal, and orthorhombic polycrystals may be easily derived. Two sets of approximate formulae are given and their ranges of validity discussed. For comparison with this static approach, we have also calculated the same quantities by simulating the polycrystal on a computer using the dynamic model developed by Middya, Basu, and Sengupta [J. Appl. Phys. 57, 1844 (1985)]. The results obtained by these two approaches based on entirely different assumptions are remarkably close to each other and to experiment for twenty‐four different noncubic polycrystalline specimens considered in the present investigation. In fact, for the effective rigidity modulus, the agreement between the two methods is within 1% in all cases except for two specimens. The reasons for this discrepancy are discussed. However, while the computer simulation provides a very simple method for evaluating the effective elastic properties of polycrystals with high accuracy, it raises a question regarding the relation between the apparently contradictory assumptions on which the static and the dynamic methods are based. Finally, an experiment is suggested that may be helpful in resolving this difficulty.