In this study, the three-dimensional wave–pile group interaction mechanism is investigated by addressing both wave behaviour and pile group responses. The Scaled Boundary Finite Element Method (SBFEM) is employed to develop the computational model. This paper, Part I of the study, mainly focuses on the theoretical development of the problem. A SBFEM model is developed to formulate both equations governing the wave motion and the structural behaviour. The proposed model, with its accuracy verified by wave interaction with a single pile foundation, is capable of addressing wave interaction with any arbitrary number of piles with various cross-sections and spatial layouts.