A drifting ice cover on the surface of the sea is considered. The ice cover consists of ice floes having various sizes, shapes, and strength properties. For sufficiently rapid and small compressive-tensile loads, each ice floe behaves as an elastic body and its deformation can be described by the model of a linearly elastic Hooke body. At higher loads, the ice floes break-up [1]. If the ice floes are located uniformly on the surface of the water and the relative velocities of adjacent ice floes are small, the motion and deformation of the ice cover can be described as a continuum with a visco-elastoplastic rheology [2–4]. The plastic properties are associated with irreversible changes in the ice cover due to the shifting and breaking-up of separate ice floes as they interact and form into hummocks. The viscous properties are manifested when inelastic collisions between ice floes become the main form of interaction in a particular area of the sea surface; such collisions occur where the drift velocity gradients are high and the ice cover is sufficiently sparse. Elastic stresses may arise in a compacted ice cover. A model of an ice cover with elastoplastic rheology is proposed. One-dimensional discontinuous solutions of the model equations are considered. The problem of the collision of two ice fields of different compactness and the problem of condensation of a drifting ice cover near a solid wall are solved.