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The present work is concerned with the analytical investigation of the effect of polydispersity on the elastic moduli of granular media. Empirical formulas are available for the estimation of elastic parameters of sands, especially for the shear modulus, usually as a function of the void ratio and the effective mean pressure. These relationships do not reflect the dependence of the small strain shear modulus on the granulometric material properties and especially on the non-uniformity index. This dependence is however strong as shown by experimental results. In the present work it is attempted to derive this qualitative dependence analytically, so as to provide a better understanding of the observations. Two different forms of granulometric curves are considered and the small strain moduli derived for isotropic and triaxial compression. In spite of the purely theoretical nature of the approach, the results are in good agreement with the experiments. A simplified formula is suggested, to facilitate application. [ABSTRACT FROM AUTHOR]