This chapter examines a benchmark nonlinearly coupled deterministic fluid-structure interaction (FSI) problem, where the fluid domain evolves in time based on the structure’s deformation, introducing geometric nonlinearity. Unlike linearly coupled models, the coupling conditions are evaluated at the current fluid-structure interface, making the problem more complex since the domain is unknown a priori and depends on the solution itself. The Lie operator splitting method is employed to construct weak solutions in finite energy spaces, but additional difficulties arise compared to linearly coupled cases. This chapter highlights the key differences between linear and nonlinear FSI coupling.