Accidental fires present many challenging hazards to people and property. The thermal and toxic effects of fires are significantly affected by the ventilation conditions supplied to the fire. Vitiation is a consequence of limited ventilation, where the products of combustion mix with the unburned reactants prior to reaction. Vitiation results in diluting and preheating the reactants, significantly enhancing the behavior of the fire. An interesting effect of vitiation is the increased propensity of the flame to experience extinction, either locally or globally. Likewise, there are other factors that can increase the propensity for extinction, including losses due to incomplete chemical kinetics, radiation, and conduction. These extinction events have a direct impact on the thermal and toxic hazards associated with accidental fires by creating holes in the reaction surface. This research provides a detailed analysis of local flame extinction by examining the behavior of counterflow flames undergoing kinetic losses, radiation losses, and vitiation. A thorough review of flame extinction theory was conducted to determine the appropriate parameters necessary for characterizing local flame extinction conditions. Simple scaling arguments are presented to demonstrate that each of these parameters is significant in accidental fires. Counterflow methane-air diffusion flames have been studied experimentally and numerically with OPPDIF to systematically examine the effects of each parameter on local flame extinction. Furthermore, a model is presented, which uses reactant composition and temperature in the vicinity of the flame, net radiation losses from the flame, and the local scalar dissipation rate as inputs to model local extinction conditions. The proposed model is suitable for integration into Computational Fluid Dynamics (CFD) codes used to predict the hazards associated with accidental fires.