A model for the ballooning mode destabilization in the presence of a sufficiently large island is developed. This model may explain the fast MHD activity (sawtooth-like) observed on Tore Supra during LH current drive in shearless equilibrium regimes with a safety factor on axis of just less than two. A simple analytical stability criterion is derived which indicates whenever an equilibrium is stable or unstable against the ballooning mode. The model is supported by Tore Supra experimental data and may also apply in other tokamaks exhibiting nearly flat q-profiles.