Physics-based coupled fire–atmosphere models are based on approximations to the governing equations of fluid dynamics, combustion, and the thermal degradation of solid fuel. They require significantly more computational resources than the most commonly used fire spread models, which are semi-empirical or empirical. However, there are a number of fire behaviour problems, of increasing relevance, that are outside the scope of empirical and semi-empirical models. Examples are wildland–urban interface fires, assessing how well fuel treatments work to reduce the intensity of wildland fires, and investigating the mechanisms and conditions underlying blow-up fires and fire spread through heterogeneous fuels. These problems are not amenable to repeatable full-scale field studies. Suitably validated coupled atmosphere–fire models are one way to address these problems. This paper describes the development of a three-dimensional, fully transient, physics-based computer simulation approach for modelling fire spread through surface fuels. Grassland fires were simulated and compared to findings from Australian experiments. Predictions of the head fire spread rate for a range of ambient wind speeds and ignition line-fire lengths compared favourably to experiments. In addition, two specific experimental cases were simulated in order to evaluate how well the model predicts the development of the entire fire perimeter.