  This paper focusses on the von K\'{a}rm\'{a}n equations for the moderately
large deformation of a very thin plate with the convex obstacle constraint
leading to a coupled system of semilinear fourth-order obstacle problem and
motivates its nonconforming Morley finite element approximation. The first part
establishes the well-posedness of the von K\'{a}rm\'{a}n obstacle problem and
also discusses the uniqueness of the solution under an a priori and an a
posteriori smallness condition on the data. The second part of the article
discusses the regularity result of Frehse from 1971 and combines it with the
regularity of the solution on a polygonal domain. The third part of the article
shows an a priori error estimate for optimal convergence rates for the Morley
finite element approximation to the von K\'{a}rm\'{a}n obstacle problem for
small data. The article concludes with numerical results that illustrates the
requirement of smallness assumption on the data for optimal convergence rate.
