We have proposed a fluid-structure coupling approach based on fixed mesh using the level set function to analyze FSI (Fluid-Structure Interaction) problems of compressible inviscid flow and large-deformable thin shell. In this approach, we introduce interface treatment using virtual particles with the level sets and structural normal velocities in order to enforce the continuity of normal velocity at the interface on a fluid fixed mesh. In this study, it is shown that the present method is also applicable to FSI problems of incompressible viscous fluid and thin shell. Then the virtual particles also possess the structural tangent velocities to impose no-slip condition at the interface. We deal with FSI problems with finite deformation and compare the numerical results of the present method and the ALE (Arbitrary Lagrangian-Eulerian) moving mesh based scheme quantitatively.