The problem of fatigue fracture of thin layer made of elastic viscous material subjected to cyclic compression by two long parallel plates is considered. It is assumed that the incompressibility condition for elastic and viscous materials is conformed. If the width of the layer is less then its length, the problem can be considered as the plane strain problem. As a material for the layer we will consider the high elastic materials, for example, polyurethane in high elastic state. In the creep and compression experiments the force and the time intervals are determined where the material behavior can be considered as linear elastic viscous. The expressions for the current lines, the rates of displacements, and stresses are derived and there diagrams are constructed. The dimensions of the thin stratum near contact planes in which the stress condition can be considered as the state of hydrostatic pressure are determined. So on the contact planes and in the inner points inside the stratum the damage and fracture o