Hydroelasticity theory, considering the second-order fluid forces induced by the coupling of first-order wave potentials, is introduced briefly in this paper. Based on the numerical results of second-order principal coordinates induced by the difference-frequency and sum-frequency fluid forces in multidirectional irregular waves, the bending moments, as well as the vertical displacements of a floating plate used as a numerical example are obtained in an efficient manner. As the phase angle components of the multidirectional waves are random variables, the principal coordinates, the vertical displacements, and the bending moments are all random variables. Extreme values of bending moments are predicted on the basis of the theory of stationary stochastic processes. The predicted linear and nonlinear results of bending moments show that the influences of nonlinear fluid forces are different not only for the different wave phase angles, but also for the different incident wave angles. In the example very large floating structure (VLFS) considered in this paper, the influence of nonlinear fluid force on the predicted extreme bending moment may be as large as 22% of the linear wave exciting forces. For an elastic body with large rigidity, the influence of nonlinear fluid force on the responses may be larger than the first-order exciting forces and should be considered in the hydroelastic analysis.