An analysis of flame spreading over a thin solid fuel in zero-gravity environment is presented. The mathematical model includes two-dimensional Navier-Stokes' momentum, energy and species equations with a one-step overall chemical reaction. The fuel consumption rate is described by a second-order Arrhenius kinetics. The energy balance along the solid fuel consists of the conduction, convection and radiation. The surface radiative loss is found to be the dominant factor for flame extinction in the low oxygen mass fraction regime. The computed flame spread rate and standoff distance are in agreement with the experimental measurements by Olson . The flame spread rate, the flame size and the solid pyrolysis length become greater as the oxygen mass fraction increases, but the standoff distance shows an opposite trend. The flame structures are illustrated graphically showing the interaction between the flow and thermal fields and the multidimensional feature in the flame front.