SUMMARYIncompressible free-surface flow is a common assumption for the modelling of water waves. Connected with the aim to develop very large floating platforms, air chamber supported floating structures have attracted considerable research interest in the past. Such structures are carried by air entrapped in chambers formed by stiff, vertical walls. In order to model these types of structures, the interactions between surface gravity waves and compressible air must be taken into account. If the payload requirements for air chamber supported structures are low enough, the air chambers may be formed by flexible membrane cylinders. In such systems, pressure variations can lead to considerable changes in chamber volume. Therefore, the flexibility of the bounding structures must be taken into account. We present a modelling strategy to tackle the fully coupled problem of compressible gas in a flexible chamber and incompressible free-surface flow in an unbounded domain. The governing equations and boundary conditions are described and solved by the finite element method. A perfectly matched layer is used to obtain a solution for an unbounded domain. Using air chambers to support very large floating structures can significantly reduce the waveinduced forces [1]. Such air chamber systems have been initially studied under the assumptions of spatially constant pressure in chambers bounded by rigid walls [2,3]. Using a semi-analytic approach for the acoustic modes in the air chamber, Lee and Newman [4] derived a model that takes spatially varying air pressure in the rigid chamber into account. All aforementioned models rely on linearised potential theory to solve the governing Laplace equation in the water domain by means of panel methods. Deformations of the platform structure may be taken into account by the use of generalised modal coordinates [5,6].In air chamber supported platforms, the buoyancy is provided by the internal pressure in one or more chambers, which are open to the water at their lower side. The internal pressure is, therefore, proportional to the platform weight. Owning to the high payload requirement of most types of very large floating structures, like floating airports or mobile offshore bases, the air chambers in systems investigated so far [1,[5][6][7][8][9] require strong bounding walls in order to sustain the resulting high internal pressure. Therefore, the chamber walls are comparatively stiff, and the behaviour of the system is governed by the compressibility of the air in the chamber. For structures with lower payload requirements, for example, usable as offshore solar power plants, the air pressure in the supporting chambers can be just several hundred Pascal above atmospheric pressure. Therefore, it is possible to form large circular cylindrical air chambers by highly flexible membranes. In such systems, the flexibility of the bounding walls must be taken into account because air pressure variations lead to substantial changes of the chamber volume. In this paper, a mechanical model for the ...