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A floating viscoelastic composite structure with generalized elastic constraints, in which the material–structure-wave interaction induces energy dissipation, is analyzed with a novel cross-scale integrated hydro-viscoelastic model. A double-level three-dimensional (3D) representative volume element model coupling mesoscale reinforced particles to a macroscale composite structure is established to obtain the structure's viscoelastic dynamic equation. Therefore, a hydro-viscoelasticity analytical model for floating composite structures with arbitrary elastic constraints under wave action is developed in the context of potential flow theory. In the process of solving the velocity potential, the dispersion equation of the water covered by the composite structure is derived. The hydrodynamic and mechanical behaviors of the floating composite structure, including the reflection coefficient, transmission coefficient, dissipation coefficient, deflection, shear force, and bending moment, are comprehensively calculated, which depend on the cross-scale integrated effects of wave action, structural features, material characteristics, and constraint combinations. This material–structure-wave integrated model would be useful to elucidate the hydro-viscoelastic dissipation mechanism of marine structures. [ABSTRACT FROM AUTHOR]