The dynamic properties of soil are normally inferred from laboratory tests on collected samples or from empirical relations. The soil properties measured in the field can be very different from those predicted from laboratory tests. It is very difficult to determine directly in the field the variation of the shear modulus and damping with the level of excitation (level of strains). This remains today a major gap in our knowledge and our ability to conduct reliable seismic analyses. The main objective of this study is to assess the feasibility of determining reliably in situ the shear modulus and damping of the soil as functions of the level of strains, developing a method to compute these properties from the measured data and providing practical recommendations for the use of the procedure. To achieve this objective, extensive and comprehensive sets of experimental and analytical studies were conducted in parallel. Some numerical analyses were performed to provide a better understanding for performing in situ tests with the newly developed vibroseis loading systems. In addition, the dynamic response of a surface foundation in vertical vibration were studied. This dissertation mostly focuses on the numerical aspects of the problem while some experimental data are also studied and utilized. Field tests were conducted to estimate shear moduli of silty sands at two sites, the Capital Aggregate Quarry and the Texas A&M University sites. Estimated nonlinear shear moduli presented very consistent trends regardless of the analysis methods and test sites. They showed larger elastic threshold shear strains, 1.5 × 10−3 % for the Capital Aggregate Quarry site and 2 × 10−3 % for the Texas A&M University site, than the mean of shear modulus curve for cohesionless soils proposed by Seed and Idriss (1970). Estimated moduli closely followed the mean of Seed and Idriss (1970) at strains larger than 6 × 10−3 % for both sites. Internal damping ratio can also be estimated if additional data are gathered from in situ tests in the future.