We consider the problem of a thin film of fluid with a columnar mesostructure (i.e., hexagonal phase of a diblock melt) placed between two hard, flat surfaces. The columns form parallel to the surfaces and the thickness of the thin film is slightly greater than the bulk equilibrium spacing of the columns. We determine the stability of the columns to a Helfrich-Hurault instability where the columns take on an undulational mode and determine the elastic constants and critical strain for the instability.