This paper describes a numerical model for studying the suppression of co-flow diffusion flames by fine water mist. A two-continuum formulation is used in which the gas phase and the water mist are both described by equations of the eulerian form. The model is used to obtain a detail understanding of the physical processes involved during the interaction of water mist and flames. The relative contribution of various mist suppression mechanisms is studied. The effect of droplet diameter, spray injection density and velocity on water mist entrainment into the dame and flame suppression is quantified. Droplet trajectories are used to identify the regions of the flame where the droplets evaporate and absorb energy. Finally, the model is used to determine the water required for extinction, and this is reported in terms of the ratio of the water supply rate to the fuel flow rate.