This paper considers a class of variational inequalities that model the buckling of a von Karman plate clamped on a part of its boundary and lying on a flat rigid support. The existence and bifurcation results of D. Goeleven, V. H. Nguyen and M. Thera[6] rely on the Leray Schauder degree. Using the topological degree for pseudo-monotone operators of type (S+),the author establishes a more general existence result for such unilateral eigenvalue problems.