Dynamic response records of pile performance during earthquakes are limited mainly due to the challenges of recording the seismic soil–pile response. This limitation has led to an inadequacy in providing a standardized basis for the calibration and validation of the available analytical and numerical methods developed for seismic soil–pile superstructure interaction problems. To bridge this gap, a series of numerical simulations of scaled, shaking table tests of model piles in soft clay has been developed in the current study. This paper aims to accurately identify all aspects and critical parameters in the numerical simulation and propose the most suitable soil constitutive model. Three soil constitutive models are selected as advanced models for soft soil, namely, the modified Mohr–Coulomb, Drucker–Prager/cap plasticity, and Cam–clay models. Similar to the physical test case study, this numerical analysis uses dimensional analysis techniques to identify scale modelling criteria and develop a scaled soil and pile-supported structure model correctly. The 3D nonlinear numerical models are developed using the Abaqus software.