The dependence of the van der Waals force on the distance between the
atomic force microscope tip and the plane surface of the sample is cal
culated. The tip is modelled by a paraboloid with stochastic perturbat
ions of its surface. The analysis of the corresponding corrections to
the van der Waals force shows that one may use the paraboloid model of
the tip for the interpretation of all experimental data in atomic for
ce microscopy.