The large-diameter reinforced concrete pile shafts are commonly designed as an economical solution for foundation of highway bridges in soft soils. The substructure method is a widely used technique for seismic SSI analysis of pile-supported bridges due to its remarkable computational efficiency. In the substructure modelling, complex-valued impedance functions are used to represent stiffness and energy dissipation characteristics of soil-pile interaction system. While characteristics of the pile head impedance functions have been decently determined for linear soil-pile interaction, the effects of inelastic interaction on the impedance function still remain unclear. In fact, this study is an attempt to overcome the limitations of linear elastic soil and rigid soil-pile interface bonding assumptions that have been used in substructure analysis. This thesis aims to develop numerical and analytical frameworks to (i) investigate seismic response of a representative bridge superstructure supported by a large-diameter pile shaft under fully coupled inelastic soil-pile-structure interaction, and (ii) compute the equivalent-linear (EL) pile head impedance functions under the controlled dynamic and earthquake loading modes. Hence, a three-dimensional finite element (FE) model of the soil-pile system, as a rigorous direct method of SSI analysis is developed. Pile shaft lateral capacity is designed following to the AASHTO LRFD guidelines. The developed model is verified using data from centrifuge tests. In order to compute EL impedance functions from the continuum FE model, an algebraic solution is derived for the system of dynamic equilibrium equations in substructure analysis. In this frequency-domain solution, Fourier transform of force and displacement values obtained from the time-domain FE analysis are inserted, while closed-form solutions for the pile head impedance matrix is derived in terms of infinite series. Results of parametric FE analyses indicate that except for the extreme near-fault motions, the residual structural drift and the pile bending moment of the system would hardly exceed the design limits. The computed EL impedances provide insight into the damping evolution and stiffness reduction due to inelastic interaction over a frequency range of interest. As a key conclusion, it is shown that soil and interface inelasticity can drastically alter the impedance values compared to their fully elastic counterpart.