This article concerns the stability of the air-water interface subjected to a 2D attractive van der Waals stress. The physical problem models the setup of a Wilhelmy plate experiment prior to three-phase contact line formation. We present and employ an unambiguous condition to quantify the stability limit in terms of the distance of closest approach of a solid cylindrical plate of parabolic cross section to the fluid surface as a function of the strength of the van der Waals surface force and plate geometry. A numerical study spanning 4 orders of magnitude of the Hamaker constant and nearly 6 orders of magnitude of solid geometry characterizes the dependence of the stability limit on these physical parameters. Comparisons are also made with a previously published analytical condition guaranteeing a stable deformation of the fluid interface. A possible experiment for testing the theory is also described. Used together with the theory, the technique could be used as an independent means of determining system properties such as the surface tension or Hamaker constant.