This paper presents a direct simulation of low frequency combustion instabilities in premixed turbulent combustors. The simulation is based on the thin flame sheet (TFS) model proposed by Marble and Candel in their investigation of ramjet and afterburner instabilities. This model is solved numerically to allow the prediction of the flame response to any excitation. The numerical calculations are performed with an original implicit extension of a two phase Row TRAC method. The numerical properties of the scheme (dispersion, dissipation) are obtained by comparison with exact solutions in the case of acoustic wave propagations in isothermal ducts. Results obtained for reactive Rows show that stability is mainly determined by the steady flow configuration and by the interaction parameter introduced to represent the effects of pressure on the local normal flame speed. Quarter-wave excitations induce the strongest instabilities when convective perturbations travelling on the flame front couple with the acoustic oscillation. A criterion for quarter-wave instability is derived and compared with experimental results.