We present a novel approach to treat fluid‐structure interactions in a closed variational setting. The standard model is the so‐called ‘arbitrary Lagrangian‐Eulerian’ (ALE) framework. Here, the fluid is transformed into an artificial coordinate system, which fits with the Lagrangian structure system. In the fully Eulerian framework, which is the reverse to ALE, the fluid is left in its natural coordinates while structure is transformed. With this approach, very large deformations, change of topology as well as free movement of the structure can be computed. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)