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A multibody system including a drilling riser system, tensioners and a floating platform is key equipment for offshore oil and gas drilling. Most of the previous studies only focus on the drilling riser system rather than the multibody system. Mechanical characteristics of the deepwater drilling riser system cannot be analyzed accurately in a simplified model. Therefore, a three-dimensional multibody analysis program is developed. The static and dynamic characteristics of the deepwater drilling riser system under different platform motions are analyzed based on the developed program. The results show that the static displacement of the riser system with tensioners is smaller than that without tensioners, which means the tensioners can suppress the deformation of the riser system. Under surge and sway motions of the platform, the dynamic displacement of the riser system with tensioners is also smaller than that without tensioners due to the tensioner suppression effect. Besides, the heave motion induces a uniform axial vibration of the riser system, while roll and pitch motions excite the riser system to vibrate laterally. Compared with the stress amplitude due to surge and sway motions, the stress amplitude of the riser system due to heave, roll and pitch motions is relatively small but cannot be neglected.