A model which describes the physical processes of upward flame spread and fire growth on wall materials has been developed and implemented as a computer program. The computer based flame spread model simulates the fire growth along a vertical combustible wall. The vertical wall material may be heated by an imposed external heat flux and is ignited at its bottom edge with a flame from a line burner of user specified strength. The model predicts the flame spread rate, the heat release rate of the fire, the flame height, the net heat flux to the wall surface, and the time varying surface temperature. The model uses inputs developed from cone calorimeter data. The results from the model compare favorably to upward flame spread experimental results for PMMA, plywood, and vinyl-ester glass composite found in the literature.