The large deformation analysis of membrane or shell structures loaded and/or supported by liquid can be based on a finite element description for the structure only. Then in statics the effects in the liquid have to be considered by using the equations of state for the liquid, the information about the current volume and the current shape of the structure. The interaction with the structure is then modeled by a pressure resulting from the liquid always acting normal to the current wetted structural part. This description can be easily used to model the filling process without all the difficulties involved with standard discretization procedures. In addition the consistent derivation of the nonlinear formulation and the linearization for a Newton type scheme results in a particular formulation which can be cast into a very efficient solution procedure based on a sequential application of the Sherman-Morrison formula.