The available empirical relationships for maximum dynamic shear modulus (Gmax) and dynamic shear damping (Ds) at low strain amplitudes for sands are reviewed. Based on tests with dry Monterey No. 0 sand in resonant column device, new relations for Gmax and Ds are proposed. In addition, based on test data in longitudinal mode of vibration, relations for dynamic Young’s modulus (Emax) and dynamic longitudinal damping (D1) are developed for the first time. The developed relations are convenient to use as they are dimensionally correct and are applicab le for any system of units. The observed experimenial data and proposed relations are in good agreement. The proposed relations for Gmax and Ds are compared with reported relations and a difference of approximately 20% and 100% is observed in some cases for dynamic shear modulus and shear damping, respectively. More field and experimental results are warranted to put the developed relations for dynamic Young’s modulus and longitudinal damping on firm foundation.