We approximate a fluid-structure interaction eigenvalue problem by means of finite elements on quadrilateral meshes. The problem under consideration looks simple and has been the object of a wide investigation: actually, no standard numerical scheme achieves acceptable results in presence of field singularities. We consider a three-field mixed method introduced by Bathe et al. and based on rectangular meshes (see [3, 12]). Recent results show that particular care has to be taken into account when dealing with finite element approximation on general quadrilateral meshes. We present numerical experiments on several sequences of meshes which definitely show how the "local" approach has to be discarded, while the "global" approach gives reasonable results. © Springer-Verlag 2001.