The drilling riser is an important piece of equipment used to link the subsea wellhead with the drilling platform. Its operating environment is extremely complex because of the effects of ocean currents, which can cause riser overload, fatigue, leading to economic loss. Therefore, in order to improve design and prevent premature failure of drilling riser, it is important to research the mechanical response to ocean currents. The effects of tension ratio and platform deflection on the lateral displacement, bending moment, and the stress of the drilling riser are analyzed, under actual working conditions and shear flow. The results show that the bending moment and lateral displacement of the drilling riser decrease significantly and the stress of the riser increases with increasing tension ratio. There is an increase in the lateral displacement of the drilling riser and the bending moment at the lower end of the drilling riser, with an increase in the initial offset of the offshore drilling platform. However, the initial offset of the offshore drilling platform has little effect on the stress of the riser. Under shear flow conditions, the lateral displacement, bending moment, and stress initially increase, then decrease, and finally stabilize. These results can be used to improve the design of drilling riser.