Eruptive fires are one category of extreme fire behaviour. They are characterized by a sudden and unpredictable change in the fire behaviour which represents an extreme danger for people involved in firefighting. The major point is about the mechanism that turns a usual fire behaviour into an eruptive fire behaviour. Among the different explanations found in the literature, the pioneering interpretation consisting in a feedback effect caused by the convective flow induced by the fire under wind and/or slope conditions, has never been disproved with an example of fire accident. The main goal of this work lies in proposing a physical modelling of this fire induced wind. This modelling attempt is derived from the brand-new version of the Balbi model, which is a simplified physical model for surface fires at the field scale that explicitly depends on the triangle of fire (fuel bed, wind and slope). This work is a first step to the modelling of fire eruption. The model tries to represent accurately the acceleration of the fire rate of spread propagating on different sloped terrain under no-wind or weak wind conditions. It is tested against three sets of experiments carried out at the laboratory scale without external wind and against a high intensity experimental fire spreading on a steep sloped terrain and conducted under weak wind conditions in the north-western of Corsica. Some statistical tools are used to compare predicted and observed rate of spread (NMSE, Normalized Mean Square Error and MAPE, Mean Absolute Percentage Error) and to understand the model’s under-predictions or over-predictions trends (FB, Fractional Bias).