pressing of layer, strengthening, finite strain, asymptotic method. 

In the paper is considered the plane problem of pressing of an anisotropic strengthened thin layer made of a rigid material by rough slabs of arbitrary curvilinear form. For the description of the deformed state is used tensor of finite deformations, which is linked to the tensor of strain speed by objective time derivative in the sense of Cotter-Rivlin. Using the asymptotic method it is found the recurrent formulas for the components of the velocity vector, strain and stress.