In the present paper, expansion formulae for the velocity potentials and associated orthogonal modecoupling relations for 3D Laplace equation satisfying higher order boundary conditions arising in fluid structure interaction problems are derived. Characteristics of the eigensystems are derived in terms of several identities and the convergence of the developed expansion formulae is demonstrated. As an application of the expansion formulae, flexural gravity wave scattering due to a crack in a floating ice sheet is investigated. The present method of solution can be easily applied to a large class of problems in the area of wave structure interaction arising in ocean engineering and various branches of applied mathematics, mathematical physics and engineering. © 2011 The Authors 2011. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.