A truss spar, named as 'Constitution' was installed in Gulf of Mexico located at 90.58' 4.8" West Longitude and 27.17'31.9" North Latitude. Since its installation in October 2006, it has weathered multiple hurricanes. After the installation, British Maritime Technology (BMT) installed an Environmental Platform Response Monitoring System (EPRMS). The EPRMS is an integrated system collecting myriad of data that include the significant wave height and peak period of waves, the magnitude and direction of current and wind in the vicinity of the truss spar, its six-degree of freedom (6-D) motions, and tensions in its mooring lines and Top-Tension Risers. With the permission from Anadarko Petroleum Corporation (APC), these data are available to the Ocean Engineering Program at Texas A&M University (TAMU). In this study, the coupled dynamic analysis of the spar interacting with the mooring and riser systems will be performed using a numerical code, named as 'COUPLE'. 'COUPLE' was developed and is continuously expanded and improved by his former and current graduate students and Professor Jun Zhang at TAMU for the computation of the interaction between a floating structure and its mooring line/riser/tendon system in time domain. The main purpose of this study is to exam the accuracy and efficiency of 'COUPLE' in computing offshore structure motions and mooring line tensions and discuss the main issues of the computation. The numerical results will be compared with the corresponding ones obtained using another commercial software, 'Orcaflex', and the corresponding field measurement during Hurricane Ike which occurred on 12th September of 2008 and a winter storm on 9th November of 2009. The satisfactory agreement between the numerical prediction made using 'COUPLE' and field measurement are observed and presented. The results of the comparisons between 'COUPLE' with 'Orcaflex' and field measurements in this study have verified the accuracy and efficiency of 'COUPLE' in computing offshore structure motions and mooring line tensions due to its nonlinear hybrid wave model which could better estimate the second-order difference-frequency wave loading.