An unsteady two dimensional numerical model of flame spread is formulated to study the transient flame spread over thin solid fuels. The work focuses on the study of transient flame spread from a steady normal gravity flame to micro gravity flame and vice versa. The gas-phase is described by two-dimensional governing equations comprising of full Navier-Stokes equations for laminar flow along with the conservation equations of mass, energy and species. The specie equations are for fuel vapor, oxygen, carbon dioxide and water vapor. A one-step, second-order finite rate Arrhenius reaction between fuel vapor and oxygen is assumed. The thin solid fuel model comprises of equations of continuity and energy in the one-dimension parallel to the solid fuel surface along with a solid fuel pyrolysis law. The solid fuel considered here is an aerodynamically and thermally thin cellulosic material. The solid is assumed to burn ideally i.e. it vaporizes to form fuel vapors without melting. The radiation transport is modeled by two-dimensional Radiative Transfer Equation, which is solved using Discrete Ordinates Method. The system of coupled partial differential equations for the flow and combustion in the gas phase is solved numerically using SIMPLER algorithm with a single step multi-grid technique for faster convergence. In normal gravity to zero-gravity transition the flame spread rate peaks (V_f = 5.96 cm/s) above steady state spread rate at zero gravity (5.32cm/s) at about 1.5 second and then decreases slowly to the steady state value (with in 5%) at about 3 seconds. Thus the experiments conducted in short duration (2s or less) drop tower may not reach steady state in the time available. On the other hand in 0g-1g transition steady state reached by about 1s. In both cases flame spread transient was oscillatory due to different response time of gas and solid phases. This was reflected in the phase behavior that the instantaneous spread rate and the integrated net heat flux in the preheat region were not in phase.