In Chapter 3, expansion formulae for wave structure interaction problems are derived based on suitable utilisation of Green’s function. In the present chapter, the use of the boundary integral equation method will be demonstrated by considering the surface wave diffraction by a flexible floating membrane. Using the free surface Green’s function, the boundary value problems associated with the wave structure interaction problems are converted to integro-differential equations in the cases of both finite and infinite water depths. The integrodifferential equations are reduced to a system of equations by two different approaches. From the solution of the system of equations, various physical quantities of interest associated with the physical problem can be obtained.