Based on the moving particle semi-implicit (MPS) method, an equivalent momentum transfer method was developed to solve the interaction between fluid and rigid structures, and the solitary wave generation was numerically simulated using the water level difference method and box-dropping method. In this method, the structure is discretized to rigid body particle groups, which are replaced by corresponding fluid particle groups. After solving the momentum equation of the single-density fluid in the entire domain, the momentum obtained by these fluid particle groups is transferred to their corresponding rigid particle groups, and the initial geometric configuration of the rigid body is restored, thus completing the dynamic coupling motion process between the fluid and structure. The numerical simulation results show that the flow field change near the structure, wave propagation, and structural motion during the solitary wave generation process simulated by this method are in good agreement with the results of physical modeling experiments. Compared with the box-dropping method, the water level differences method can generate solitary waves with greater height and faster propagation speed, but it needs more time to generate stable solitary waves.