The effect of fine-water droplets in extinguishing steady, laminar counterflow methane-air nonpremixed dames is investigated here, using a numerical approach. A new two-phase model using a hybrid Eulerian-Lagrangian formulation for the gas-droplet flow is developed as part of this work. A key feature of the model developed is that it can avoid the singularity associated with the droplet number density equation in a consistent manner by using a Lagrangian equation for droplet flux fraction. The gas phase is described by a detailed model involving full chemical kinetics and transport, whereas droplet evaporation and heat transfer are modeled assuming quasisteady conditions. Application of the model to several monodisperse sizes of water droplets, ranging from 5-50 mu m, revealed an interesting nonmonotonic dependence of the flame extinction strain rate on droplet size. This phenomenon is attributed to the droplet dynamics in the counterflow field considered here and to the resulting nonmonotonic heat sink associated with mass evaporation observed at the oxygen-consumption or radical production layer of the flame.