There has been substantial development in computer codes for three-dimensional linear hydroelasticity, but to the authors’ knowledge, there are no problems of sufficient complexity put forth in the open literature to serve as appropriate benchmark problems for a floating structure. We present in this paper detailed descriptions of two such problems for three-dimensional hydroelastic computer codes. The first structure is a rectangular, box-shaped “barge” with dimensions 100 m10 m2 m. The second is a Wigley hull with dimensions 100 m10 m4.5 m. In both cases, the deformational response is primarily global. Detailed descriptions of each structure, the finite element structural shell models, and the hydrodynamic fluid models, based on the constant panel Green’s function method, are provided. Fine meshes are used to minimize discretization errors. Detailed results, including dry natural periods and modes, wet natural periods, and wave-induced displacements and stresses, are presented. The detail is sufficient for others to use the problems as benchmarks for computer codes.