Bridges are an essential part of lifeline infrastructure, and their performance during earthquakes is critical. Therefore, it is crucial to design their foundations effectively to withstand the lateral loads generated during such events. However, the traditional approach of modeling the caisson-pier-deck system as a single-degree-of-freedom system neglects the rigidity arising due to the pier-deck connection. Past studies have highlighted the importance of considering pier-deck joint rigidity while analyzing the integrated system of soil, foundation, pier, and deck for earthquake loading. This study employs finite element analysis to simulate the response of a caisson and pier subjected to seismic loads. The study provides insights into the design of caisson foundation-supporting bridge structures and highlights the need to consider pier-deck joint stiffness to achieve optimal seismic performance. The analysis is carried out for different levels of pier-deck joint rigidity, modeled as a rotational spring with varying stiffness. The analysis results highlight the variation in the responses generated on the pier and caisson due to the introduction of rigidity. It is observed that the responses generated are significantly higher on the pier than in the caisson due to pier-deck joint rigidity.