The ignition phenomena of a solid fuel plate of polymethyl-methacrylate (PMMA), which is vertically positioned and exposed to a thermal radiation source, is numerically studied here. A two-dimensional transient model includes such various aspects as thermal decomposition of PMMA, gas phase radiation absorption, chemical reaction and air entrainment by natural convection. Whereas the previous studies consider the problem approximately in a one-dimensional geometry by neglecting the natural convection, the present model takes account of two-dimensional effect of radiation and air entrainment. The inert heating of the solid fuel is also taken into consideration. Radiative heat transfer is incorporated by the Discrete Ordinates Method (DOM) with local absorption coefficient evaluated with corresponding gas species concentrations. The thermal history of solid fuel plate shows a good agreement compared with experimental results. Despite of induced natural convective flow that takes away heat from the fuel surface, the locally absorbed radiant energy, which is eventually converted to the internal energy, is found to play an important role in the onset of gas phase ignition. The ignition is considered to occur when the rate of variation of gas phase reaction rate reaches its maximum value. Once the ignition takes place, the flame propagates downward. Then the effects of incident radiant intensity and gas phase absorption coefficient on the ignition are discussed.