For the physical model of wildland fire spread, errors or discrepancies in the prediction of spread rate may arise from uncertain, imprecise or improper determinations of the model parameters due to unreasonable assumptions, rough approximations, or inaccurate measurements. In this study, a parametric uncertainty analysis is made on a typical model of upslope fire spread that is consistent with many other models in the framework of the heat transfer theory and the major equations of sub-models. The variation ranges of the model parameters are determined based on the experimental data and assumptions, thereby the rate of fire spread (ROS) is used as a target variable of model calculation to evaluate the response of the model to parametric uncertainties. It is found that the values of ignition temperatures and averaged flame temperatures have significant impacts on the predicted values of ROS under lower slopes. Although the impacts decrease with the increase of slope, they are still non-negligible under higher slopes. Especially under lower slopes, the assumed values of both temperatures have significant effects on model prediction. The error in estimating the flame length has a remarkable influence on model prediction, and especially, the flame length variation of the same magnitude results in consistent relative errors under different slopes. A larger fluctuation range around a fixed average flame length results in a greater deviation from the predicted results, while for the same fluctuation range of flame length, the relative errors under higher slope angles are distinctly greater than those under lower slopes. In contrast, the errors for evaluation of the flame tilt angle have negligible effects on model predictions. The flame emissivity has a remarkable effect on model prediction and thus should be adjusted to better characterize the variation of flame intensity under different slopes. Besides, the prediction of ROS is very sensitive to the evaluation of fuel consumption efficiency, especially for higher slope angles. Simulation results indicate that larger heat convection coefficients are required for achieving better prediction results for higher slope angles, which agrees well with the previous experimental finding that with the increase of slope angle, a kind of flame-induced convection plays a more and more important role in fire spread.