A numerical study was made on the time-dependent ignition process of a horizontally placed solid fuel heated by external radiation. As soon as the solid starts to be heated, a hot plume with combustible fuel is ejected into the oxygen-containing atmosphere to be mixed and to react leading to a spontaneous ignition. The effects of gravity and ambient oxygen concentration on the ignition behavior were studied. The numerical model is a two-dimensional axisymmetric configuration with time-dependent heat and mass transport process and one-step exothermic reaction for gas phase, and three-step degradative reactions for solid phase. An appropriate ignition criterion was introduced to define ignition delay time and position. It was found that an increase in the gravity tends to prevent the ignition by increasing heat loss from the hot fuel-gas plume, whereas an increase in the ambient oxygen concentration enhances the ignition by accelerating chemical reaction in the plume. The two distinct types of ignition were identified in gravity vs, ambient oxygen concentration plot; the first one occurs when the oxygen concentration is relatively high and is ignited at the tip of the plume with a short ignition delay time, while the second one occurs when the oxygen concentration is low and is ignited at the inside of the plume with a relatively long delay time. The former type of ignition was found to be controlled basically by 1-D heat and mass transport process, whereas the latter type is controlled by the 2-D process caused by buoyancy-induced flow.