A numerical model for flame spread over polymeric surfaces is constructed. The dependence of the flame spread rate on phase change and thermal properties is investigated by varying three non-dimensional parameters, (S) over bar St, (k) over bar (t), and (C) over bar (Pt). Quantitative comparisons indicate that the numerical model provides excellent agreement to an analytical formula in the cases of variable latent heat of the phase change, variable liquid thermal capacity, and variable thermal conductivity. However, the deRis formula yields a constant spread rate higher than the numerical result and is independent of phase change. Qualitatively, with the increase of Sr, or with the decrease of (k) over bar (t) or C-Pt, the flame spread rate increases. In addition, (k) over bar (t) is the strongest determinant of the influence of the thickness of the liquid region. The mechanisms of flame spread at the steady state are interpreted by applying an energy balance principle for the control volume upstream of the flame leading edge. It is found that a ratio between the total heat applied to the condensed material upstream of the flame leading edge and the spread rate reveals the physical mechanisms that control the preheating of the condensed material to the ignition temperature. The dependence of flame structure on St, (k) over bar (t), and (C) over bar (Pt) is studied. It is found that with the increase of St or (k) over bar, or with the decrease of (C) over bar (Pt), the size of the flame increases. These results indicate that flame size dependence follows the magnitude of the spread rate when the properties of the condensed material are variable. (C) 2001 by The Combustion Institute.