The installation of a topside structure can be categorized into the following stages: start, pre-lifting, lifting, lifted, rotating, positioning, lowering, mating, and end of installation. The transfer of the module onto the floating spar hull occurs in the last three stages, from lowering to the end. The coupled multi-body motions are calculated in both calm water and in irregular waves with a significant wave height (1.52m). The effects of the hydrodynamic interactions between the heavy lifting vessel and the spar hull during the lowering and mating stages are considered. The internal forces caused by the load transfer and ballasting are derived for the mating phases. The results of the internal forces for the calm water condition are compared with those in the irregular sea condition. Although the effect of the pitch motion on the relative vertical motion between the deck of the floating structure and the topside module is significant in the mating phases, the internal force induced pitch motion is too small to have this influence. However, the effect of the internal force on the wave-induced heave responses in the mating phases is noticeable in the irregular sea condition because transfer mass-induced draught changes for the floating structure are observed to have higher amplitudes than the external force induced responses. The impacts of the module on the spar hull in the mating phase are investigated.