The development of disturbances to a plane, premixed flame front under the action of an externally imposed pressure gradient, has been studied numerically in two spatial demensions. The flow has been modelled well into the non-linear regime in which a thin spike of unburnt gas penetrates into the burnt region. Even though the length scales of the applied pressure disturbances considered are very large compared to the flame width, the results show that the dominant mechanism in the early stages is the Rayleigh-Taylor effect. Variations of Lewis number are found to have very little effect on the progress of the interaction. Changes in the flame Mach number and disturbance wavelength are also investigated.