This paper investigates the nonlinear soil-pile-structure interaction (SPSI) employing three-dimensional (3D) nonlinear finite element models (FEM) verified with the results of large-scale shaking table tests of model pile groups-superstructure systems. The responses of piles in both liquefiable and non-liquefiable soil sites to ground motion with varying intensities were evaluated considering both kinematic and inertial interaction. The calculated piles and soil responses agreed well with the responses measured during the shaking events. The numerical models correctly predicted the different pile deformation modes that were exhibited in the experiments. The finite element analysis (FEA) was then employed to perform a parametric study to evaluate the kinematic and inertial effects on the piles' response, considering different ground motion levels and piles characteristics. It was found that the bending moment of piles in the liquefiable site increases significantly, compared to the non-liquefiable site, due to the loss of lateral support of the liquified soil, and the maximum bending moment occurs at the interface between the liquified and liquefied sand layers. The inertial interaction contributes the most to the bending moments at the pile top and the interface between the top clay and liquefied loose sand layers. For piles with a larger diameter, the bending moment due to kinematic interaction increases significantly, and the bending moment distribution corresponds to short (rigid) pile behaviour. In addition, the piles at the saturated site displace laterally as a rigid body during strong ground motions because the pile base loses the lateral support due to the soil liquefaction. Finally, the kinematic interaction effect becomes more significant for piles with higher elastic modulus.