We present a computational model to describe the two-phase thermal and chemical interactions between a freely propagating premixed flame and fine droplets of water. The objective is to develop a fundamental understanding of flame structure and extinction in the presence of a water mist. The model and the computational algorithm must accommodate strong coupling between the droplet dynamics and the gaseous flow. The gas-phase conservation equations, which include elementary chemistry, are discretized and solved on an adaptive Eulerian mesh, while the droplet dynamics are represented in a Lagrangian framework. A modified arclength-continuation method is used to follow the solutions through the extinction turning point and thus predict flame-extinction limits. The model predicts how burning velocity and extinction conditions depend on droplet size and number density. The results compare very favorably with previously published theoretical analyses.