Horizontally unstretchable continuum of the Westergaard's type is mode
lled by elastic layers of finite thicknesses interconnected with very
thin, flexible but unstretchable sheets. For the regular layered struc
ture, the finite difference equations are formulated and their closed
solutions is presented. The resulting formulae are used when the conta
ct problem solution is sought in a form of series of spherical functio
ns. The unknown series coefficients are determined via Galerkine metho
d, the formulae for punch settlement and inclination are presented and
a numerical procedure is developed and used to study the influence of
the Westergaard's subgrade material parameters epsilon (subgrade rein
forcement intensity) and v (Poisson's ratio of the basic material).