Interaction between violent water waves and structures is of a major concern and one of the important issues that has not been well understood in marine engineering. This paper will present first attempt to extend the Meshless Local Petrov Galerkin method with Rankine source solution (MLPG_R) for studying such interaction, which solves the Navier–Stokes equations for water waves and the elastic vibration equations for structures under wave impact. The MLPG_R method has been applied successfully to modeling various violent water waves and their interaction with rigid structures in our previous publications. To make the method robust for modeling wave elastic–structure interaction (hydroelasticity) problems concerned here, a near-strongly coupled and partitioned procedure is proposed to deal with coupling between violent waves and dynamics of structures. In addition, a novel approach is adopted to estimate pressure gradient when updating velocities and positions of fluid particles, leading to a relatively smoother pressure time history that is crucial for success in simulating problems about wave–structure interaction. The developed method is used to model several cases, covering a range from small wave to violent waves. Numerical results for them are compared with those obtained from other methods and from experiments in literature. Reasonable good agreement between them is achieved.