The dynamic response of a large number of uniform-sized, dry sands and a limited number of improved gradations was obtained from resonant column tests, and the data were analyzed to evaluate the effects of grain characteristics (size, gradation, shape, surface texture) and other test variables (e.g., ambient stress conditions, void ration or relative density, strain amplitude, number of loading cycles) on the dynamic shear modulus and the damping capacity. The test results indicate that mean principal stress, density, and strain amplitude exert the strongest influence on both the modulus and damping capacity. Shear modulus is further influenced by roundness (used to characterize shape); the effects of the other parameters are either virtually zero or very small. Damping capacity is essentially independent of roundness and the other parameters, but it is influenced by the number of loading cycles. The test results were evaluated using multiple linear regression analysis, and empirical relationships correlating shear modulus and damping capacity to the important controlling parameters were obtained. The applicability of these relationships on other sands was assessed in a secondary testing program utilizing six different sand samples. The proposed relationships and relationships proposed by other investigators were compared with the experimental data. /Author/