The study of Fluid Structure Interaction (FSI) is becoming of great interest in many engineering applications. In this work we propose a new model to study the deformation of solid structures induced by a two-phase flow. We use a monolithic approach for the FSI problem while a Volume Of Fluid method (VOF) is considered for the reconstruction and advection of the interface. A PLIC method based on the ELVIRA algorithm for the reconstruction and a split algorithm for the interface advection is used. For an accurate reconstruction of the interface a huge number of computational elements are required and a multilevel algorithm coupled to an efficient compression-expansion technique is developed to reduce computational costs and memory requiremen...