Nowadays, an increasing number of ships and marine structures are manufactured and inevitably operated in rough sea. As a result, some phenomena related to the violent fluid-elastic structure interactions (e.g., hydrodynamic slamming on marine vessels, tsunami impact on onshore structures, and sloshing in liquid containers) have aroused huge challenges to ocean engineering fields. In this paper, the moving particle semi-implicit (MPS) method and finite element method (FEM) coupled method is proposed for use in numerical investigations of the interaction between a regular wave and a horizontal suspended structure. The fluid domain calculated by the MPS method is dispersed into fluid particles, and the structure domain solved by the FEM method is dispersed into beam elements. The generation of the 2D regular wave is firstly conducted, and convergence verification is performed to determine appropriate particle spacing for the simulation. Next, the regular wave interacting with a rigid structure is initially performed and verified through the comparison with the laboratory experiments. By verification, the MPS-FEM coupled method can be applied to fluid-structure interaction (FSI) problems with waves. On this basis, taking the flexibility of structure into consideration, the elastic dynamic response of the structure subjected to the wave slamming is investigated, including the evolutions of the free surface, the variation of the wave impact pressures, the velocity distribution, and the structural deformation response. By comparison with the rigid case, the effects of the structural flexibility on wave-elastic structure interaction can be obtained.