Two-dimensional vertical impact of a rigid blunt body onto a floating ice plate is studied. The problem is coupled and unsteady. The liquid is inviscid, incompressible, and of infinite depth. The ice floe is modeled as a thin viscoelastic plate of constant thickness. The plate edges are free of bending stresses and shear forces. The upper surface of the plate is covered with a viscoelastic layer of constant small thickness and negligible inertia. The reaction force of this soft layer is predicted by a nonlinear and one-dimensional Winkler-Kelvin-Voigt model, which does not permit a contact between the rigid body and the ice plate. The soft layer may describe either the presence of snow on the ice or a layer of crushed ice in the place of impact, or can be considered as a way of regularization of problems with concentrated loads. The rigid body touches the upper surface of the soft layer and then suddenly starts to move downward with constant velocity. It is shown that the strains in the ice plate caused by the impact are weakly dependent on the characteristics of the soft layer. The magnitudes and distributions of the strains are studied depending on the length of the ice plate, retardation time of the ice model, thickness of the plate, shape of the rigid body, place of impact, and the impact speed. The value of the retardation time in the soft layer model is discussed with relation to the ice crushing by impact.