Researches and developments of VLFSs for airport use and so on have been carried out for recent years. There is a VLFS which has a pontoon type floating structure supported with many dolphins and it is important to investigate sufficiently the behaviors of such VLFS under earthquake loading. In this paper, a floating structure supported with 49 dolphins was modeled as both a horizontally elastic plate and rigid plate supported with springs and dashpots through gap elements. The time history response analyses of the structure when the gaps between fenders and dolphins were equal to zero were performed with varying the period and the velocity of the applied sinusoidal waves as an earthquake loading and the following conclusions have been obtained. 1. The floating structure oscillates transversely with their natural periods of sway and yaw irrespective of the periods of sinusoidal earthquake wave applied, though the transverse oscillation is overlapped with an oscillation, of which period is the same as that of sinusoidal earthquake wave applied. 2. The floating structure has resonance with the sinusoidal earthquake wave not only in the modes of sway and yaw but also in the modes of two and more nodes elastic vibration due to the horizontal elasticity of the structure. The fender, dolphin and ground also have resonance. 3. When the sinusoidal earthquake wave velocity is relatively low, the resonance in the mode of yaw appears and the fender and dolphin reaction forces in the mode of yaw become larger than those in the mode of sway. 4. An equation is proposed to estimate the sinusoidal earthquake wave velocity that the strong resonance of the floating structure with the sinusoidal earthquake wave in the mode of yaw and two and more nodes elastic vibration of the floating structure. 5. Resonance periods of the fender, dolphin and ground are obtained accurately from the vibration equation on spring and dashpot and the resonance period of floating structure in the mode of sway is obtained as equal to that of fender. 6. Within the low period region where dolphin and ground have resonance with the sinusoidal earthquake wave, the fender and dolphin reaction forces are not affected by the horizontal elasticity of the floating structure and the sinusoidal earthquake wave velocity.