A Deep Draft Semi-submersible(DDS) under certain flow conditions could be subjected to Vortex-Induced Motions(VIM), which significantly influences the loads on and life fatigue of the moorings and the risers. To investigate the VIM of a DDS with four rectangular section columns in waves coupled with a uniform current, a numerical study using the computational fluid dynamics(CFD) method was conducted. The issues of the VIM of multi-column floaters can be conveniently converted to the issues of oscillating cylinders in fluid cross flows. This paper looks into the CFD numerical simulation of infinite cylinders having rectangular sections in a two-dimensional sinusoidal timedependent flow field coupled with a uniform current. The resulted hydrodynamic forces and motion responses in different oscillatory flows plus currents both aligned in the same direction for the incidence of 135° of the DDS relative to the flow are compared with the ones in current only cases. The results show that the VIM response of this geometric arrangement of a DDS with four rectangular columns in a current combined with oscillatory flows is more evident than that in the current only case. The oscillatory flows and waves have the significant influence on the VIM response, forces and trajectory, in-plane motions of the DDS. A Deep Draft Semi-submersible (DDS) under certain flow conditions could be subjected to Vortex-Induced Motions (VIM), which significantly influences the loads on and life fatigue of the moorings and the risers. To investigate the VIM of a DDS with four rectangular sections columns in waves coupled with a uniform current, a numerical study using the computational fluid dynamics (CFD) method was conducted. The issues of the VIM of multi-column floaters can be conveniently transferred to the issues of oscillating cylinders in fluid cross flows . This paper looks into the CFD numerical simulation of infinite cylinders with rectangular sections in a two-dimensional sinusoidal time dependent flow field coupled with a uniform current. The resulting hydrodynamic forces and motion responses in different oscillatory flows plus currents both aligned in the same direction for the incidence of 135 ° of the DDS relative to the flow are compared with the ones in current only cases. The results show that the VIM response of this geometric arrangement of a DDS with four rectangular columns in a current combined with oscillatory flows is more evident than that in the current only case. The oscillatory flows and waves have the significant influence on the VIM response, forces and trajectory, in -plane motions of the DDS.