Two-dimensional axisymmetric simulation of stoichiometric methane-air flames stabilized on flat burners at elevated pressure is reported in the present work. Such flames, in practice, are experimentally obtained using the heat flux method for measurement of laminar burning velocity of fuel-oxidizer mixtures (Bosschaart and de Goey, 2004; Goswami et al., 2013). The method makes use of a burner with a perforated brass burner plate. The dimensions of such a plate play an important role in creating flat flames. The present investigation is focused on studying laminar premixed flame structure numerically at elevated pressure up to 15 bar using a one-step and a detailed chemical reaction mechanism. Three burner plate models (of varying hole diameter and porosity) are used in the simulations for pressures up to 7 bar with a one-step mechanism. The surface area increase of the flame was evaluated based on an isotherm at 900 K and the net reaction rate of methane compared to a flat flame. The comparison of these models shows that the surface area increase can significantly be reduced by choosing a smaller hole diameter and larger porosity. The results of the detailed simulations using an appropriate chemical reaction mechanism up to 15 bar using a burner plate model, which is similar to the ones used in experiments (mentioned above), show a nonlinear increase of the flame curvature with elevating pressure. A hole diameter of 0.25 mm and a pitch of 0.29 mm is suggested for a burner plate in such experiments. Flame structure at elevated pressure is also analyzed further based on species profiles obtained.