The linear stability of radially bounded thinning free films is examined for the case in which the surfaces of the film are initially plane and parallel. The two-dimensional time-dependent drainage flow computed by lubrication theory constitutes the base state. The linear stability of this flow with respect to axially symmetric varicose disturbance is treated in the quasistatic approximation. For thin films, disperse London-van der Waals attractive forces play a key role in determining the critical thickness at rupture, and the results are presented as predictions of critical film aspect ratio as a function of two dimensionless groups which are ratios of the important physical-chemical forces on the film. Predicted critical thicknesses are seen to agree well with the limited available experimental data.