One of the concepts for the design of very large floating airports, is to build a very large mat-like structure, that is kept on station by means of anchor lines or by means of a dynamic positioning system. One of the advantages of this kind of structure is that it can be towed towards its temporary destination. Ohkusu and Nanba (1996, Proceedings of the 16th International Workshop on Water Waves and Floating Bodies, Hiroshima University, Japan) presented an asymptotic theory to describe the deflection of the platform due to relatively short incident waves while it is positioned in shallow water. Due to the fact that the vertical dimension is averaged out it is relatively simple to derive a valid formulation. Hermans (1997, van Groesen, E., Soewono, E. (Eds.), Differential Equations Theory, Numerics and Applications. Kluwer Academic, Dordrecht, pp. 103-125) derived a formulation for deep water. Unfortunately, this formulation uses some nonphysical boundary conditions and its applicability is questionable for this reason. Later, Hermans (2000) derived an exact differential-integral formulation for the deflection. In the latter paper, the problem is solved numerically. In a subsequent paper, this differential-integral equation is used to obtain a short-wave solution for the homogeneous semi-infinite platform, positioned in deep water. In this paper, the method is extended to the determination of the deflection of short waves of a platform of general shape and inhomogeneous elastic properties. The authors explain how the 'ray method' can be used to describe the deflection, due to short waves, of a very large floating platform in finite or infinite water depth. The elastic properties of the platform are isotropic, but may be distributed inhomogeneously. In the first section, a derivation of the equation for the phase and amplitude functions is given. Then an integro-differential equation for the determination of the deflection is used to find the initial condition for amplitude along the characteristics. For the homogeneous two-dimensional platform in water of finite depth, an exact solution in the form of a superposition of modes can be obtained. This simplified problem serves as a 'canonical' problem for problems with the same structure locally. In the last section, the authors give some result for a semi-infinite platform with varying elasticity coefficient, the mass distribution being taken constant.