The nonlinear hydroelastic interaction between a solitary wave and a submerged box with elastic upper surface plate is investigated in a 2D numerical wave flume. The objective is to investigate how hydroelasticity affects the interaction process. The numerical wave flume solves incompressible Navier-Stokes equations with a Volume-of-Fluid method for free surface simulation. The linear elastic structure dynamic equations are solved by a Finite Element Method, and embedded into the solution of flow field by using a monolithic fluid-structure interaction algorithm. The numerical method is thoroughly verified against existing experiments and numerical simulations. A series of numerical tests are conducted, which contains free vibrations of the plate, and the interaction between solitary waves and submerged boxes with various wave amplitudes and submerged depths. Results obtained with and without considering hydroelasticity are compared to investigate the influence of hydroelastic effect on the wave load, the structure response and the flow field. Fast Fourier Transform and wavelet transform are adopted to reveal the oscillatory features of the interaction process. Some meaningful conclusions are drawn, such as hydroelasticity changes the amplitude and period of the oscillatory motion and the variation of the oscillatory frequency can be approximated by a simple still water prediction method.