The authors consider a pontoon type flexible floating airport as the very large floating structure. In order to design this kind of structure, we have to investigate several key points in advance. Among those key points, estimation of the wave drift forces is very important in order to design of the mooring system. In this paper, the authors consider the square type flexible flat plate with shallow draft, exactly speaking, zero draft as the floating airport. The authors develop the computer code of the slowly varying wave drift force for an elastic floating structure with shallow draft based on the so called Near Field Method which is validated by both the Far Field Method and the corresponding Experiments. The authors conclude that even though the water depth is shallower, there is no big difference among the steady wave drift forces in each water depth, while the rigidity of the structure is smaller, more flexible, then, the steady wave drift forces or mooring forces are smaller. Finally, they showed the flexibility of a floating structure decreases not only steady wave drift forces but also slowly varying wave drift forces under the numerical time domain simulation of a very large floating structure with the multiple dolphins mooring system.