In this study, a combination of the smoothed particle hydrodynamics (SPH) and finite element method (FEM) solving the complex problem of interaction between fluid with free surface and an elastic structure is studied. A brief description of SPH and FEM is presented. Contact mechanics is used for the coupling between fluid and structure, which are simulated with SPH and FEM, respectively. In the proposed method, to couple meshfree and mesh-based methods, fluid and structure are solved together by a complete stiffness matrix instead of iterative predictive-corrective or master-slave methods. In addition, fully dynamic large-deformation analysis is carried out in FEM by taking into account mass and damping of the elastic structure. Accordingly, a two-dimensional fluid-structure interaction (FSI) code is developed and validated with two different experiments available in the literature. The results of the numerical method are in good agreement with the experiments. In addition, a novel laboratory experiment on a dam break problem with elastic gate in which the length of the initial water column is larger than its height is conducted. The main difference between the previous experiments and the one conducted in this study is that an upward water motion parallel to the elastic gate is observed at the upstream side of the gate. This motion is captured with the numerical method.