A system of von Karman equations for a nanoplate has been generalized by introducing effective tangential and flexural stiffnesses and elastic moduli, with regard to surface elasticity and residual surface stresses on the outer surfaces. A modified Kirsch problem was solved for the case of an infinite nanoplate with a circular hole under plane stress in terms of effective elastic moduli. Two forms of local stability loss in this problem and the corresponding critical load for two different elastic characteristics of all plate surfaces were determined numerically and analytically. The dependence of the effective stiffnesses and elastic moduli on the plate thickness, and of the critical load on the hole radius (size effect) was discussed.