This paper presents an aero-hydro-elastic model of a semi-submersible floating wind turbine. A specific attention is drawn to hydrodynamic modeling options and their effect on the dynamic response of the platform. The NREL 5 MW reference wind turbine mounted on the historical concept of semi-submersible platform Dutch tri-floater is considered. A specific hydrodynamic model of loads on a semi-submersible platform is used within the wind turbine design code FAST from NREL. This hydrodynamic model includes nonlinear hydrostatic and Froude-Krylov forces, diffraction/radiation forces obtained from linear potential theory, and Morison forces to take into account viscous effects on the braces and damping plates. The effect of the different hydrodynamic modeling options is investigated. As one could have expected, it is found that the effect of viscous drag on braces, and nonlinear Froude-Krylov loads, becomes larger with increasing wave height. Their effect remains of small order. Simulations also are run with directional waves, it is found that wave directionality induces larger transverse motions.