In atomic force microscope studies of molecular thin films, a defined jump of the tip through the film is often observed once a certain threshold force has been exceeded. Here, we present a theory to describe this film rupture and to relate microscopic parameters to measurable quantities. We assume that the tip has to overcome an activation energy before the film ruptures. A universal relation between the force dependence of the activation energy and the approaching velocity of the tip is derived. Two complementary models for calculating the activation energy are presented: a continuum nucleation model and a discrete molecular model. Both models predict a narrow distribution of yield forces in agreement with experimental results.