ABSTRACT A numerical study on the spontaneous ignition process of a vertically placed solid thin fuel heated by external radiation in normal gravity, quiescent environment was made. The ambient oxygen mass fraction is varied from 35 % down to the non-ignition limit. It was found that in the non-ignition case, the maximum reaction rate and maximum temperature in gas-phase were too weak to onset the combustion reaction. For the ambient oxygen concentration greater than 17 % the ignition and transition to flame spread all are achievable. The low ambient oxygen concentration has larger and stronger ignited flame than the high ambient oxygen concentration at the instant of ignition occurs. The flame grows rate was found faster than the purely opposed and purely concurrent spread flames. Although it has smaller ignited flame, the propagating flame in high ambient oxygen concentration becomes longer and stronger in structure than the low oxygen flame. The results reveal that, the flame grows rate in transition increase with the increasing in ambient oxygen concentration.