The aim of this paper is to introduce a fully nonlinear numerical finite element solver for the simulation of nonlinear wave processes in the presence of a solid ice sheet. In this study, solid ice cover referred to the size of the ice sheet and denoted that the length of the ice sheet was many times larger than the longest relevant wavelength. The complexity of the ice sheet characteristics was assumed to be homogeneous, isotropic and in the linear elastic plate regime so that the deformation process could be modeled by the Kirchhoff–Love plate ansatz. The method presented was verified and validated for different ice dimensions and wave scenarios. At the beginning, the implementation of the flexural rigidity to the free surface boundary condition was verified by comparing the analytical wave-ice dispersion relation to simulation results with small amplitude regular waves and varying ice dimensions. Afterwards, the general applicability was validated by means of wave-ice experiments. The experiments were performed in the ice tank at Hamburg Ship Model Basin HSVA comprising regular waves and transient wave groups.