In this study the effects of finite-rate chemistry arc included in a model of flame spread over solid fuels. The gas-phase reaction mechanism is described by the one-step reaction F+ viO→P and the gas-phase fluid-dynamic configuration consists of an opposed flow with a linear velocity gradient. The assumption of local circular symmetry near the flame front reduces the equations for conservation of species and energy in the gas to nonlinear ordinary differential equations. The spreading flame is modeled as a premixed flame arc followed by a diffusion flame. The Damkohler number D and the nondimcnsional activation energy β are the important finite-rate parameters in this model. When D→ ∞ the predictions of the finite-rate model reduce lo the predictions of the previous heat transfer model of Wichman (1983). The theoretical predictions compare favorably with previous experimental results for laboratory-scale flame spread over thermally-thick sheets of polymethylmethacrylate (PMMA) over the entire Damköhler-number range of the data.