  Accurate asymptotic solutions are presented for axisymmetric deformation of
thin layers constrained by either two rigid plates or two rigid spheres. Those
solutions are developed using Saint-Venant's principle and the layer thinness
as the only assumptions. The solutions are valid in the entire range of
Poisson's ratios, and allow one to distinguish among compressible, nearly
incompressible, and incompressible layers. That classification involves both
material and geometric parameters.
