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The process of downward flame spread over the thin bed of combustible material is studied numerically by solving two-dimensional steady-state conservation equations. The algorithm for the prediction of flame spread rate is based on the principle of minimal entropy production. The primary purpose of investigation is focused on the influence of opposed ambient flow (forced and buoyancy) on the flame spread behavior. Achieved results showed the appropriate evaluation, in comparison with experimental data, of the overall effect of the opposed flow and of the limit of stable flame propagation.