We investigate two cases where thin liquid films give rise to non-classical undercompressive shock profiles due to the interplay of the driving forces with surface tension. In the first, a liquid layer is driven up an inclined plane by a Marangoni shear stress, and the evolution of the film thickness is determined by a single fourth order PDE. Undercompressive shocks can arise in two different scenarios and explain important features of the experimental observation. In the second case, we look at dewetting of moderately thin films from a very hydrophobic substrate, described by a shallow-water type system of equations.