This work forms part of an investigation into the nonlinear interaction between steep (but not overturning) transient waves and flared structures, using a coupled finite element and boundary element model. The use of a coupled approach is based on consideration of the relative strengths and weaknesses of the finite element (FE) and boundary element (BE) methods when implemented separately (e.g., efficiency of computation versus complexity of adaptive mesh generation). A FE model can be used to advantage away from the body, where the domain is regular, and a BE discretization near the body where the moving mesh is complex. This paper describes the aspects of the FE and BE models which have been developed for this analysis, each based on the use of quadratic isoparametric elements implemented in a mixed Eulerian–Lagrangian formulation. Initially, the two approaches have been developed side by side, in order to ensure the use of robust components in the coupled formulation. Results from these methods are obtained for a series of test cases, including the interaction of an impulse wave with a circular cylinder in a circular tank, and nonlinear diffraction by a cylinder in a long tank.