In this paper, a numerical model coupling the smoothed particle hydrodynamics (SPH) with peridynamics (PD) is developed to solve the problem of the hydroelastic water entry. By combining the geometric nonlinear peridynamics with the weakly compressible SPH, the proposed model can efficiently simulate the nonlinear deformation of the structure and the deformation of a fluid free surface. The transmission of information between the fluid and solid phases is implemented by a dummy particle boundary treatment method. By simulating benchmark tests, the ability of the proposed model to solve nonlinear fluid–structure coupling problems is verified. In order to improve the computational efficiency, the graphics processing unit parallel acceleration scheme is applied to the SPH-PD model. Compared with the serial scheme, the speedup effect of the parallel scheme in large-scale computation is verified. As an application of the numerical model, the water entry of the flexible panel at a constant entry velocity is studied. The mechanism of hydroelastic effect is explained by analyzing the variations in the fluid pressure field, slamming force, and panel deformation during water entry. In addition, the influences of plate rigidity, impact velocity, and deadrise angle on the hydroelastic effect are investigated.