We consider the dynamics of an elastic sheet as it starts to adhere to a wall, a process
that is limited by the viscous squeeze flow of the intervening liquid. Elastohydrodynamic lubrication theory allows us to derive a partial di↵erential equation coupling
the elastic deformation of the sheet, the microscopic van der Waals adhesion, and
viscous thin film flow. We use a combination of numerical simulations of the governing equation and a scaling analysis to describe the self-similar touchdown of the sheet
as it approaches the wall. An analysis of the equation in terms of similarity variables
in the vicinity of the touchdown event shows that only the fundamental similarity
solution is observed in the time-dependent numerical simulations, consistent with
the fact that it alone is stable. Our analysis generalizes similar approaches for
rupture in capillary thin film hydrodynamics and suggests experimentally verifiable
predictions for a new class of singular flows linking elasticity, hydrodynamics, and
adhesion