The elastic-viscous Maxwell’s equations for aging media are formulated. Investigations of the mechanical properties of polyurethane in the experiments on creep and pressure on the specimens without aging and with the climate and deformation aging were carried out. The problem of thin layer made of incompressible viscous material subjected to compression by two long parallel plates is considered. The stress diagrams for the unaged and aged materials are constructed. It is shown, that on the surface and inside of the pressed layer the state of hydrostatic pressure is occurred. The received results can be applied to estimate the strength of different elastic viscous materials (natural and artificial rubbers, polyurethane, asphaltic concrete) and the items where these materials are used as working elements, for example, tires, roads, the pressing shafts with the rubber or polyurethane cover and others. Refs 3. Figs 10.