The focus of this paper is on numerical modelling of methanol liquid pool fires. A mathematical model is first developed to describe the evaporation and burning of a two-dimensional or axisymmetric pool containing pure liquid methanol. Then, the complete set of unsteady, compressible Navier-Stokes equations for reactive flows are solved in the gas phase to describe the convection of the fuel gases away from the pool surface, diffusion of the gases into the surrounding air and the oxidation of the fuel into product species. Heat transfer into the liquid pool and the metal container through conduction, convection and radiation are modelled by solving a modified form of the energy equation. Clausius–Clapeyron relationships are invoked to model the evaporation rate of a two-dimensional pool of pure liquid methanol. The governing equations along with appropriate boundary and interface conditions are solved using the flux-corrected transport algorithm. Numerical results exhibit a flame structure that compares well with experimental observations. Temperature profiles and burning rates were found to compare favourably with experimental data from single- and three-compartment laboratory burners. The model predicts a puffing frequency of approximately 12 Hz for a 1 cm diameter methanol pool in the absence of any air co-flow. It is also observed that increasing the air co-flow velocity helps in stabilizing the diffusion flame, by pushing the vortical structures away from the flame region.