Surface-stabilized combustion burners or surface-radiant burners use perforated ceramic plates, ceramic foams, or metal fibers to stabilize a premixed flame. These burners are the most straightforward alternative to have both, the benefits of the reactant preheating technique and a great amount of heat transferred by radiation from the burner to the load. However, in its design, one of the greatest difficulties is to predict the flame stability limits; especially under operating conditions that lead to flashbacks and blowouts. This work presents a computational methodology based on the finite volume method with a two-dimensional domain to predict the flame curvature towards the unburned and burned gas that occurs before flashback and blowout, respectively. In the methodology, continuity, momentum, energy, and chemical species equations are solved to obtain the increase in the surface area of the flame. It was observed that this value can be used as a criterion to predict whether an operating condition is stable. When comparing the numerical results with experimental results reported in the literature, good predictions of the operating conditions that lead to flashbacks and blowouts are observed