This paper attempts to explain the motion behaviour of the marine riser coupled to a drill string when the vortex induced vibration (VIV) is involved. Vibrations have been reported to have a major effect on the drilling performance, affecting the rate of penetration (ROP), causing severe damages to the drilling tools and also reduces the efficiency of the drilling process. There are two major components of drilling tools that are subjected to vibration, namely the marine riser and the drilling string. Analysis of vibration in the marine riser and drill string are two topical areas that have individually received considerable attention by researchers in the past. Though these two subjects are interrelated, borne by the fact that the marine riser encapsulates and protects the drill pipe, there have been few attempts to investigate them together as a unity. Due to the complexities of the models, simplified assumptions were made in order to undertake the investigation by using staggered approach. The results were compared with the experimental and simulation data from the open literature. It was found that the maximum displacement with negative damping occurs at low frequency and rotation speed. © (2014) Trans Tech Publications, Switzerland.