This study deals with the computation of parameterized reduced order models for hydroelastic vibrations of interior fluid–structure systems with a free surface. The main parameter is the weight of the liquid acting on the structure, which allows static and dynamic simulations for different liquid heights in a tank. Both the structure and the liquid domains are mapped in reference configurations, which constituted a first originality of the paper. The second originality of the proposed approach consists in using projections on an eigenmode basis associated with the use of an adapted SVD in order to compute the eigenfrequencies of the coupled problem. In particular, we show that the proposed approach allows to construct reduced order model involving a small number of matrices through a decomposition of linearized reduced operators in terms of separated parameters functions. Convergence analysis of numerical results is discussed showing the efficiency of the method.