A preventive approach to fire safety is proper material selection based on the flammability characteristics. One such measure of flammability is the limiting oxygen index (LOI). This is a commonly used numerical flammability index for relative grading and selecting materials. The test measures the extinction limit of a downward spreading flame over a finite size (rectangular slab or rod) fuel specimen. In this work, a two-dimensional numerical model was used to study the flame stabilization and extinction characteristics over a thick model solid fuel, which resembles a specimen burning near extinction limit in an LOI testing procedure. The computations were preformed for a mixed buoyant-forced-flow environment prevailing in the LOI test at normal gravity. At sufficiently high oxygen level (far away from flame extinction limit) the flame is anchored on the sides of the fuel slab (side-stabilized flame), but as the oxygen level is reduced, at a certain value the flame stabilization point abruptly shifts from the sides of the specimen to the wake region (wake flame). The structural details of these two modes of flame stabilization are discussed. The computations also show that the shift in the flame-anchoring position with oxygen level exhibits hysteresis; i.e., multiple flame solutions may exist for a given environmental condition of flow and oxygen. The flame extinction limits and flame-shift limits (side-stabilized flame to wake flame and vice versa) in ambient oxygen percentage are presented for different forced-flow velocities. Over the velocity range studied here, the side-stabilized flame (similar to flames over of thin fuels) becomes less flammable (higher LOI) at higher velocity, whereas the wake-stabilized flame becomes more flammable (lower LOI) with increase in forced-flow velocity. To understand the implication of this earth-based measurement to material selection for space application, additional computations were performed for pure forced-flow environment in zero gravity. Stabilization and extinction behavior of the flames at normal gravity are compared with those in zero gravity. The computations in a pure forced-flow environment show that the two modes are also present in a zero-gravity environment but only above certain minimum flow velocity. Below this velocity only the single flaming solution was obtained. In the present computations, the LOI values at zero gravity were lower than those at normal gravity. For zero gravity the LOI based on side-stabilized flame (for thin fuels) shows a nonmonotonic behavior: there is a minimum LOI which for the present set of property and kinetic parameter values occurs at a forced velocity of about 3-5 cm/s. For zero gravity the LOI based on wake flame extinction decreases rapidly with flow velocity for small velocities but with further increase in velocity the LOI value stays approximately constant. © 2006 The Combustion Institute.