This thesis presents the comparative study of the three different dynamic analysis methods (quasi-static, frequency-domain, time-domain), with respect to the dynamic analysis of the Yme MOPUstor platform. The initiation of this thesis is Allseas engineering project. As a major contractor in the oil and gas industry, Allseas group is seeking a transformation and tries to redefine herself in the platform decommissioning business. With the new built platform installation / decommissioning and pipe-lay vessel Pioneering Spirit, Allseas group is well prepared to execute her first decommissioning project, the decommissioning of the Yme MOPUstor platform. The Yme MOPUstor is a production jack up platform, located in the North Sea. It was built and installed in 2010. However, due to its obvious dynamic defects, this platform is abandoned and will be decommissioned in 2015. After the abandon of the platform, several institutions were invited to investigate the dynamic behavior of the Yme MOPUstor. However, different conclusions are given by using different dynamic analysis methods. For the purpose of the decommissioning, it is inevitable to judge those existing studies and carry out a new dynamic analysis. Therefore, this thesis is motivated by this important and interesting challenge. This comparative study is carried out in four aspects: the linear versus non-linear, the quasi-static versus dynamic, the stochastic versus deterministic and the efficiency. The comparative study is first demonstrated on some sample models to illustrate the fundamental differences. Then, the dynamic analyses of the Yme MOPUstor for the given sea states by using different methods are analyzed and compared. In addition of the comparative study, a new dynamic analysis method, the higher order frequency domain method (HFD), is developed and verified. This new method is believed to significantly improve both the accuracy and the efficiency of the traditional methods. Besides, the HFD method also provides an approach to better understanding the fundamental differences between the traditional quasi-static, frequency domain and time-domain methods.