Abstract: Based on the linear potential flow theory, the flow field is divided into three sections： incident potential and reflection potential, memory section of radiation potential and transient section of the radiation potential. The time-dependent elastic deflection of a vertical elastic plate is described by the mode-expansion method, the velocity potential is solved by using Fourier transform and Laplace transform, and the implicit 4th-order Runge-Kutta scheme with uniform time step is applied to solve the coupled motions of an elastic plate and fluid. First, with an initial condition that the elastic plate is bent, the comparative results are in good agreement with corresponding linear analytical solution and numerical solution. Second, the hydroelastic vibration of a vertical elastic plate induced by the pulse wave is considered, and the effects of the elastic plate stiffness coefficient, mass coefficient, pulse amplitude and edge conditions on hydroelastic behavior are studied systematically. Finally, the following conclusions have been obtained： the stiffness coefficients have a great impact upon the vibration frequency; the vibration amplitude values have a positive correlation with the pulse amplitude values; and the fatigue damage of the vertical elastic plate is the most severe when the plate is fixed on both sides.