SPARs (or column-type offshore platforms) are a kind of common platforms in the Oil and Gas exploration industries. Nowadays due to financial and technical reasons, these platforms are one of the most usual offshore platforms, so the analysis methods of their design are rapidly being developed, improved and modified. In this research, we have evaluated the motion behavior and the response of SPARs induced by waves by means of analytical capabilities of MOSES software. MOSES is a powerful computational tool for any system which can be placed in the fluid and can cope with variety of complex and time-consuming analyses (precisely and rapidly), such as Time Domain, Frequency Domain and Coupled analyses. In this research the concept of Dynamic Instability of SPARs which hadn't been able to be evaluated completely by common types of software, have been considered and estimated by MOSES software. As well, various developed geometric hull forms (compared to simple-classical hull forms) have been considered in order to obtain the improved and better motion responses (especially at Heave response). Both Time Domain and Frequency Domain analyses have been performed, and the consistency of results confirms the accuracy. With Coupled analysis, the values of responses have decreased due to the added damping produced by simultaneous modeling of platform's hull, Mooring and Risers systems.